diff -r 69928a704ffb -r 7afc121e0689 lemon/lp_base.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/lp_base.h	Tue Dec 02 21:40:33 2008 +0100
@@ -0,0 +1,1705 @@
+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library.
+ *
+ * Copyright (C) 2003-2008
+ * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
+ * (Egervary Research Group on Combinatorial Optimization, EGRES).
+ *
+ * Permission to use, modify and distribute this software is granted
+ * provided that this copyright notice appears in all copies. For
+ * precise terms see the accompanying LICENSE file.
+ *
+ * This software is provided "AS IS" with no warranty of any kind,
+ * express or implied, and with no claim as to its suitability for any
+ * purpose.
+ *
+ */
+
+#ifndef LEMON_LP_BASE_H
+#define LEMON_LP_BASE_H
+
+#include<iostream>
+#include<vector>
+#include<map>
+#include<limits>
+#include<lemon/math.h>
+
+#include<lemon/core.h>
+#include<lemon/bits/lp_id.h>
+
+///\file
+///\brief The interface of the LP solver interface.
+///\ingroup lp_group
+namespace lemon {
+
+  /// Function to decide whether a floating point value is finite or not.
+
+  /// Retruns true if the argument is not infinity, minus infinity or NaN.
+  /// It does the same as the isfinite() function defined by C99.
+  template <typename T>
+  bool isFinite(T value)
+  {
+    typedef std::numeric_limits<T> Lim;
+    if ((Lim::has_infinity && (value == Lim::infinity() || value ==
+                               -Lim::infinity())) ||
+        ((Lim::has_quiet_NaN || Lim::has_signaling_NaN) && value != value))
+    {
+      return false;
+    }
+    return true;
+  }
+
+  ///Common base class for LP solvers
+
+  ///\todo Much more docs
+  ///\ingroup lp_group
+  class LpSolverBase {
+
+  protected:
+
+    _lp_bits::LpId rows;
+    _lp_bits::LpId cols;
+
+  public:
+
+    ///Possible outcomes of an LP solving procedure
+    enum SolveExitStatus {
+      ///This means that the problem has been successfully solved: either
+      ///an optimal solution has been found or infeasibility/unboundedness
+      ///has been proved.
+      SOLVED = 0,
+      ///Any other case (including the case when some user specified
+      ///limit has been exceeded)
+      UNSOLVED = 1
+    };
+
+      ///\e
+    enum SolutionStatus {
+      ///Feasible solution hasn't been found (but may exist).
+
+      ///\todo NOTFOUND might be a better name.
+      ///
+      UNDEFINED = 0,
+      ///The problem has no feasible solution
+      INFEASIBLE = 1,
+      ///Feasible solution found
+      FEASIBLE = 2,
+      ///Optimal solution exists and found
+      OPTIMAL = 3,
+      ///The cost function is unbounded
+
+      ///\todo Give a feasible solution and an infinite ray (and the
+      ///corresponding bases)
+      INFINITE = 4
+    };
+
+    ///\e The type of the investigated LP problem
+    enum ProblemTypes {
+      ///Primal-dual feasible
+      PRIMAL_DUAL_FEASIBLE = 0,
+      ///Primal feasible dual infeasible
+      PRIMAL_FEASIBLE_DUAL_INFEASIBLE = 1,
+      ///Primal infeasible dual feasible
+      PRIMAL_INFEASIBLE_DUAL_FEASIBLE = 2,
+      ///Primal-dual infeasible
+      PRIMAL_DUAL_INFEASIBLE = 3,
+      ///Could not determine so far
+      UNKNOWN = 4
+    };
+
+    ///The floating point type used by the solver
+    typedef double Value;
+    ///The infinity constant
+    static const Value INF;
+    ///The not a number constant
+    static const Value NaN;
+
+    static inline bool isNaN(const Value& v) { return v!=v; }
+
+    friend class Col;
+    friend class ColIt;
+    friend class Row;
+
+    ///Refer to a column of the LP.
+
+    ///This type is used to refer to a column of the LP.
+    ///
+    ///Its value remains valid and correct even after the addition or erase of
+    ///other columns.
+    ///
+    ///\todo Document what can one do with a Col (INVALID, comparing,
+    ///it is similar to Node/Edge)
+    class Col {
+    protected:
+      int id;
+      friend class LpSolverBase;
+      friend class MipSolverBase;
+      explicit Col(int _id) : id(_id) {}
+    public:
+      typedef Value ExprValue;
+      typedef True LpSolverCol;
+      Col() {}
+      Col(const Invalid&) : id(-1) {}
+      bool operator< (Col c) const  {return id< c.id;}
+      bool operator> (Col c) const  {return id> c.id;}
+      bool operator==(Col c) const  {return id==c.id;}
+      bool operator!=(Col c) const  {return id!=c.id;}
+    };
+
+    class ColIt : public Col {
+      const LpSolverBase *_lp;
+    public:
+      ColIt() {}
+      ColIt(const LpSolverBase &lp) : _lp(&lp)
+      {
+        _lp->cols.firstFix(id);
+      }
+      ColIt(const Invalid&) : Col(INVALID) {}
+      ColIt &operator++()
+      {
+        _lp->cols.nextFix(id);
+        return *this;
+      }
+    };
+
+    static int id(const Col& col) { return col.id; }
+
+
+    ///Refer to a row of the LP.
+
+    ///This type is used to refer to a row of the LP.
+    ///
+    ///Its value remains valid and correct even after the addition or erase of
+    ///other rows.
+    ///
+    ///\todo Document what can one do with a Row (INVALID, comparing,
+    ///it is similar to Node/Edge)
+    class Row {
+    protected:
+      int id;
+      friend class LpSolverBase;
+      explicit Row(int _id) : id(_id) {}
+    public:
+      typedef Value ExprValue;
+      typedef True LpSolverRow;
+      Row() {}
+      Row(const Invalid&) : id(-1) {}
+
+      bool operator< (Row c) const  {return id< c.id;}
+      bool operator> (Row c) const  {return id> c.id;}
+      bool operator==(Row c) const  {return id==c.id;}
+      bool operator!=(Row c) const  {return id!=c.id;}
+    };
+
+    class RowIt : public Row {
+      const LpSolverBase *_lp;
+    public:
+      RowIt() {}
+      RowIt(const LpSolverBase &lp) : _lp(&lp)
+      {
+        _lp->rows.firstFix(id);
+      }
+      RowIt(const Invalid&) : Row(INVALID) {}
+      RowIt &operator++()
+      {
+        _lp->rows.nextFix(id);
+        return *this;
+      }
+    };
+
+    static int id(const Row& row) { return row.id; }
+
+  protected:
+
+    int _lpId(const Col& c) const {
+      return cols.floatingId(id(c));
+    }
+
+    int _lpId(const Row& r) const {
+      return rows.floatingId(id(r));
+    }
+
+    Col _item(int i, Col) const {
+      return Col(cols.fixId(i));
+    }
+
+    Row _item(int i, Row) const {
+      return Row(rows.fixId(i));
+    }
+
+
+  public:
+
+    ///Linear expression of variables and a constant component
+
+    ///This data structure stores a linear expression of the variables
+    ///(\ref Col "Col"s) and also has a constant component.
+    ///
+    ///There are several ways to access and modify the contents of this
+    ///container.
+    ///- Its it fully compatible with \c std::map<Col,double>, so for expamle
+    ///if \c e is an Expr and \c v and \c w are of type \ref Col, then you can
+    ///read and modify the coefficients like
+    ///these.
+    ///\code
+    ///e[v]=5;
+    ///e[v]+=12;
+    ///e.erase(v);
+    ///\endcode
+    ///or you can also iterate through its elements.
+    ///\code
+    ///double s=0;
+    ///for(LpSolverBase::Expr::iterator i=e.begin();i!=e.end();++i)
+    ///  s+=i->second;
+    ///\endcode
+    ///(This code computes the sum of all coefficients).
+    ///- Numbers (<tt>double</tt>'s)
+    ///and variables (\ref Col "Col"s) directly convert to an
+    ///\ref Expr and the usual linear operations are defined, so
+    ///\code
+    ///v+w
+    ///2*v-3.12*(v-w/2)+2
+    ///v*2.1+(3*v+(v*12+w+6)*3)/2
+    ///\endcode
+    ///are valid \ref Expr "Expr"essions.
+    ///The usual assignment operations are also defined.
+    ///\code
+    ///e=v+w;
+    ///e+=2*v-3.12*(v-w/2)+2;
+    ///e*=3.4;
+    ///e/=5;
+    ///\endcode
+    ///- The constant member can be set and read by \ref constComp()
+    ///\code
+    ///e.constComp()=12;
+    ///double c=e.constComp();
+    ///\endcode
+    ///
+    ///\note \ref clear() not only sets all coefficients to 0 but also
+    ///clears the constant components.
+    ///
+    ///\sa Constr
+    ///
+    class Expr : public std::map<Col,Value>
+    {
+    public:
+      typedef LpSolverBase::Col Key;
+      typedef LpSolverBase::Value Value;
+
+    protected:
+      typedef std::map<Col,Value> Base;
+
+      Value const_comp;
+    public:
+      typedef True IsLinExpression;
+      ///\e
+      Expr() : Base(), const_comp(0) { }
+      ///\e
+      Expr(const Key &v) : const_comp(0) {
+        Base::insert(std::make_pair(v, 1));
+      }
+      ///\e
+      Expr(const Value &v) : const_comp(v) {}
+      ///\e
+      void set(const Key &v,const Value &c) {
+        Base::insert(std::make_pair(v, c));
+      }
+      ///\e
+      Value &constComp() { return const_comp; }
+      ///\e
+      const Value &constComp() const { return const_comp; }
+
+      ///Removes the components with zero coefficient.
+      void simplify() {
+        for (Base::iterator i=Base::begin(); i!=Base::end();) {
+          Base::iterator j=i;
+          ++j;
+          if ((*i).second==0) Base::erase(i);
+          i=j;
+        }
+      }
+
+      void simplify() const {
+        const_cast<Expr*>(this)->simplify();
+      }
+
+      ///Removes the coefficients closer to zero than \c tolerance.
+      void simplify(double &tolerance) {
+        for (Base::iterator i=Base::begin(); i!=Base::end();) {
+          Base::iterator j=i;
+          ++j;
+          if (std::fabs((*i).second)<tolerance) Base::erase(i);
+          i=j;
+        }
+      }
+
+      ///Sets all coefficients and the constant component to 0.
+      void clear() {
+        Base::clear();
+        const_comp=0;
+      }
+
+      ///\e
+      Expr &operator+=(const Expr &e) {
+        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
+          (*this)[j->first]+=j->second;
+        const_comp+=e.const_comp;
+        return *this;
+      }
+      ///\e
+      Expr &operator-=(const Expr &e) {
+        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
+          (*this)[j->first]-=j->second;
+        const_comp-=e.const_comp;
+        return *this;
+      }
+      ///\e
+      Expr &operator*=(const Value &c) {
+        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
+          j->second*=c;
+        const_comp*=c;
+        return *this;
+      }
+      ///\e
+      Expr &operator/=(const Value &c) {
+        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
+          j->second/=c;
+        const_comp/=c;
+        return *this;
+      }
+
+    };
+
+    ///Linear constraint
+
+    ///This data stucture represents a linear constraint in the LP.
+    ///Basically it is a linear expression with a lower or an upper bound
+    ///(or both). These parts of the constraint can be obtained by the member
+    ///functions \ref expr(), \ref lowerBound() and \ref upperBound(),
+    ///respectively.
+    ///There are two ways to construct a constraint.
+    ///- You can set the linear expression and the bounds directly
+    ///  by the functions above.
+    ///- The operators <tt>\<=</tt>, <tt>==</tt> and  <tt>\>=</tt>
+    ///  are defined between expressions, or even between constraints whenever
+    ///  it makes sense. Therefore if \c e and \c f are linear expressions and
+    ///  \c s and \c t are numbers, then the followings are valid expressions
+    ///  and thus they can be used directly e.g. in \ref addRow() whenever
+    ///  it makes sense.
+    ///\code
+    ///  e<=s
+    ///  e<=f
+    ///  e==f
+    ///  s<=e<=t
+    ///  e>=t
+    ///\endcode
+    ///\warning The validity of a constraint is checked only at run time, so
+    ///e.g. \ref addRow(<tt>x[1]\<=x[2]<=5</tt>) will compile, but will throw 
+    ///an assertion.
+    class Constr
+    {
+    public:
+      typedef LpSolverBase::Expr Expr;
+      typedef Expr::Key Key;
+      typedef Expr::Value Value;
+
+    protected:
+      Expr _expr;
+      Value _lb,_ub;
+    public:
+      ///\e
+      Constr() : _expr(), _lb(NaN), _ub(NaN) {}
+      ///\e
+      Constr(Value lb,const Expr &e,Value ub) :
+        _expr(e), _lb(lb), _ub(ub) {}
+      ///\e
+      Constr(const Expr &e,Value ub) :
+        _expr(e), _lb(NaN), _ub(ub) {}
+      ///\e
+      Constr(Value lb,const Expr &e) :
+        _expr(e), _lb(lb), _ub(NaN) {}
+      ///\e
+      Constr(const Expr &e) :
+        _expr(e), _lb(NaN), _ub(NaN) {}
+      ///\e
+      void clear()
+      {
+        _expr.clear();
+        _lb=_ub=NaN;
+      }
+
+      ///Reference to the linear expression
+      Expr &expr() { return _expr; }
+      ///Cont reference to the linear expression
+      const Expr &expr() const { return _expr; }
+      ///Reference to the lower bound.
+
+      ///\return
+      ///- \ref INF "INF": the constraint is lower unbounded.
+      ///- \ref NaN "NaN": lower bound has not been set.
+      ///- finite number: the lower bound
+      Value &lowerBound() { return _lb; }
+      ///The const version of \ref lowerBound()
+      const Value &lowerBound() const { return _lb; }
+      ///Reference to the upper bound.
+
+      ///\return
+      ///- \ref INF "INF": the constraint is upper unbounded.
+      ///- \ref NaN "NaN": upper bound has not been set.
+      ///- finite number: the upper bound
+      Value &upperBound() { return _ub; }
+      ///The const version of \ref upperBound()
+      const Value &upperBound() const { return _ub; }
+      ///Is the constraint lower bounded?
+      bool lowerBounded() const {
+        return isFinite(_lb);
+      }
+      ///Is the constraint upper bounded?
+      bool upperBounded() const {
+        return isFinite(_ub);
+      }
+
+    };
+
+    ///Linear expression of rows
+
+    ///This data structure represents a column of the matrix,
+    ///thas is it strores a linear expression of the dual variables
+    ///(\ref Row "Row"s).
+    ///
+    ///There are several ways to access and modify the contents of this
+    ///container.
+    ///- Its it fully compatible with \c std::map<Row,double>, so for expamle
+    ///if \c e is an DualExpr and \c v
+    ///and \c w are of type \ref Row, then you can
+    ///read and modify the coefficients like
+    ///these.
+    ///\code
+    ///e[v]=5;
+    ///e[v]+=12;
+    ///e.erase(v);
+    ///\endcode
+    ///or you can also iterate through its elements.
+    ///\code
+    ///double s=0;
+    ///for(LpSolverBase::DualExpr::iterator i=e.begin();i!=e.end();++i)
+    ///  s+=i->second;
+    ///\endcode
+    ///(This code computes the sum of all coefficients).
+    ///- Numbers (<tt>double</tt>'s)
+    ///and variables (\ref Row "Row"s) directly convert to an
+    ///\ref DualExpr and the usual linear operations are defined, so
+    ///\code
+    ///v+w
+    ///2*v-3.12*(v-w/2)
+    ///v*2.1+(3*v+(v*12+w)*3)/2
+    ///\endcode
+    ///are valid \ref DualExpr "DualExpr"essions.
+    ///The usual assignment operations are also defined.
+    ///\code
+    ///e=v+w;
+    ///e+=2*v-3.12*(v-w/2);
+    ///e*=3.4;
+    ///e/=5;
+    ///\endcode
+    ///
+    ///\sa Expr
+    ///
+    class DualExpr : public std::map<Row,Value>
+    {
+    public:
+      typedef LpSolverBase::Row Key;
+      typedef LpSolverBase::Value Value;
+
+    protected:
+      typedef std::map<Row,Value> Base;
+
+    public:
+      typedef True IsLinExpression;
+      ///\e
+      DualExpr() : Base() { }
+      ///\e
+      DualExpr(const Key &v) {
+        Base::insert(std::make_pair(v, 1));
+      }
+      ///\e
+      void set(const Key &v,const Value &c) {
+        Base::insert(std::make_pair(v, c));
+      }
+
+      ///Removes the components with zero coefficient.
+      void simplify() {
+        for (Base::iterator i=Base::begin(); i!=Base::end();) {
+          Base::iterator j=i;
+          ++j;
+          if ((*i).second==0) Base::erase(i);
+          i=j;
+        }
+      }
+
+      void simplify() const {
+        const_cast<DualExpr*>(this)->simplify();
+      }
+
+      ///Removes the coefficients closer to zero than \c tolerance.
+      void simplify(double &tolerance) {
+        for (Base::iterator i=Base::begin(); i!=Base::end();) {
+          Base::iterator j=i;
+          ++j;
+          if (std::fabs((*i).second)<tolerance) Base::erase(i);
+          i=j;
+        }
+      }
+
+      ///Sets all coefficients to 0.
+      void clear() {
+        Base::clear();
+      }
+
+      ///\e
+      DualExpr &operator+=(const DualExpr &e) {
+        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
+          (*this)[j->first]+=j->second;
+        return *this;
+      }
+      ///\e
+      DualExpr &operator-=(const DualExpr &e) {
+        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
+          (*this)[j->first]-=j->second;
+        return *this;
+      }
+      ///\e
+      DualExpr &operator*=(const Value &c) {
+        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
+          j->second*=c;
+        return *this;
+      }
+      ///\e
+      DualExpr &operator/=(const Value &c) {
+        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
+          j->second/=c;
+        return *this;
+      }
+    };
+
+
+  private:
+
+    template <typename _Expr>
+    class MappedOutputIterator {
+    public:
+
+      typedef std::insert_iterator<_Expr> Base;
+
+      typedef std::output_iterator_tag iterator_category;
+      typedef void difference_type;
+      typedef void value_type;
+      typedef void reference;
+      typedef void pointer;
+
+      MappedOutputIterator(const Base& _base, const LpSolverBase& _lp)
+        : base(_base), lp(_lp) {}
+
+      MappedOutputIterator& operator*() {
+        return *this;
+      }
+
+      MappedOutputIterator& operator=(const std::pair<int, Value>& value) {
+        *base = std::make_pair(lp._item(value.first, typename _Expr::Key()),
+                               value.second);
+        return *this;
+      }
+
+      MappedOutputIterator& operator++() {
+        ++base;
+        return *this;
+      }
+
+      MappedOutputIterator operator++(int) {
+        MappedOutputIterator tmp(*this);
+        ++base;
+        return tmp;
+      }
+
+      bool operator==(const MappedOutputIterator& it) const {
+        return base == it.base;
+      }
+
+      bool operator!=(const MappedOutputIterator& it) const {
+        return base != it.base;
+      }
+
+    private:
+      Base base;
+      const LpSolverBase& lp;
+    };
+
+    template <typename Expr>
+    class MappedInputIterator {
+    public:
+
+      typedef typename Expr::const_iterator Base;
+
+      typedef typename Base::iterator_category iterator_category;
+      typedef typename Base::difference_type difference_type;
+      typedef const std::pair<int, Value> value_type;
+      typedef value_type reference;
+      class pointer {
+      public:
+        pointer(value_type& _value) : value(_value) {}
+        value_type* operator->() { return &value; }
+      private:
+        value_type value;
+      };
+
+      MappedInputIterator(const Base& _base, const LpSolverBase& _lp)
+        : base(_base), lp(_lp) {}
+
+      reference operator*() {
+        return std::make_pair(lp._lpId(base->first), base->second);
+      }
+
+      pointer operator->() {
+        return pointer(operator*());
+      }
+
+      MappedInputIterator& operator++() {
+        ++base;
+        return *this;
+      }
+
+      MappedInputIterator operator++(int) {
+        MappedInputIterator tmp(*this);
+        ++base;
+        return tmp;
+      }
+
+      bool operator==(const MappedInputIterator& it) const {
+        return base == it.base;
+      }
+
+      bool operator!=(const MappedInputIterator& it) const {
+        return base != it.base;
+      }
+
+    private:
+      Base base;
+      const LpSolverBase& lp;
+    };
+
+  protected:
+
+    /// STL compatible iterator for lp col
+    typedef MappedInputIterator<Expr> ConstRowIterator;
+    /// STL compatible iterator for lp row
+    typedef MappedInputIterator<DualExpr> ConstColIterator;
+
+    /// STL compatible iterator for lp col
+    typedef MappedOutputIterator<Expr> RowIterator;
+    /// STL compatible iterator for lp row
+    typedef MappedOutputIterator<DualExpr> ColIterator;
+
+    //Abstract virtual functions
+    virtual LpSolverBase* _newLp() = 0;
+    virtual LpSolverBase* _copyLp(){
+      LpSolverBase* newlp = _newLp();
+
+      std::map<Col, Col> ref;
+      for (LpSolverBase::ColIt it(*this); it != INVALID; ++it) {
+        Col ccol = newlp->addCol();
+        ref[it] = ccol;
+        newlp->colName(ccol, colName(it));
+        newlp->colLowerBound(ccol, colLowerBound(it));
+        newlp->colUpperBound(ccol, colUpperBound(it));
+      }
+
+      for (LpSolverBase::RowIt it(*this); it != INVALID; ++it) {
+        Expr e = row(it), ce;
+        for (Expr::iterator jt = e.begin(); jt != e.end(); ++jt) {
+          ce[ref[jt->first]] = jt->second;
+        }
+        ce += e.constComp();
+        Row r = newlp->addRow(ce);
+
+        double lower, upper;
+        getRowBounds(it, lower, upper);
+        newlp->rowBounds(r, lower, upper);
+      }
+
+      return newlp;
+    };
+
+    virtual int _addCol() = 0;
+    virtual int _addRow() = 0;
+
+    virtual void _eraseCol(int col) = 0;
+    virtual void _eraseRow(int row) = 0;
+
+    virtual void _getColName(int col, std::string & name) const = 0;
+    virtual void _setColName(int col, const std::string & name) = 0;
+    virtual int _colByName(const std::string& name) const = 0;
+
+    virtual void _setRowCoeffs(int i, ConstRowIterator b,
+                               ConstRowIterator e) = 0;
+    virtual void _getRowCoeffs(int i, RowIterator b) const = 0;
+    virtual void _setColCoeffs(int i, ConstColIterator b,
+                               ConstColIterator e) = 0;
+    virtual void _getColCoeffs(int i, ColIterator b) const = 0;
+    virtual void _setCoeff(int row, int col, Value value) = 0;
+    virtual Value _getCoeff(int row, int col) const = 0;
+    virtual void _setColLowerBound(int i, Value value) = 0;
+    virtual Value _getColLowerBound(int i) const = 0;
+    virtual void _setColUpperBound(int i, Value value) = 0;
+    virtual Value _getColUpperBound(int i) const = 0;
+    virtual void _setRowBounds(int i, Value lower, Value upper) = 0;
+    virtual void _getRowBounds(int i, Value &lower, Value &upper) const = 0;
+
+    virtual void _setObjCoeff(int i, Value obj_coef) = 0;
+    virtual Value _getObjCoeff(int i) const = 0;
+    virtual void _clearObj()=0;
+
+    virtual SolveExitStatus _solve() = 0;
+    virtual Value _getPrimal(int i) const = 0;
+    virtual Value _getDual(int i) const = 0;
+    virtual Value _getPrimalValue() const = 0;
+    virtual bool _isBasicCol(int i) const = 0;
+    virtual SolutionStatus _getPrimalStatus() const = 0;
+    virtual SolutionStatus _getDualStatus() const = 0;
+    virtual ProblemTypes _getProblemType() const = 0;
+
+    virtual void _setMax() = 0;
+    virtual void _setMin() = 0;
+
+
+    virtual bool _isMax() const = 0;
+
+    //Own protected stuff
+
+    //Constant component of the objective function
+    Value obj_const_comp;
+
+  public:
+
+    ///\e
+    LpSolverBase() : obj_const_comp(0) {}
+
+    ///\e
+    virtual ~LpSolverBase() {}
+
+    ///Creates a new LP problem
+    LpSolverBase* newLp() {return _newLp();}
+    ///Makes a copy of the LP problem
+    LpSolverBase* copyLp() {return _copyLp();}
+
+    ///\name Build up and modify the LP
+
+    ///@{
+
+    ///Add a new empty column (i.e a new variable) to the LP
+    Col addCol() { Col c; _addCol(); c.id = cols.addId(); return c;}
+
+    ///\brief Adds several new columns
+    ///(i.e a variables) at once
+    ///
+    ///This magic function takes a container as its argument
+    ///and fills its elements
+    ///with new columns (i.e. variables)
+    ///\param t can be
+    ///- a standard STL compatible iterable container with
+    ///\ref Col as its \c values_type
+    ///like
+    ///\code
+    ///std::vector<LpSolverBase::Col>
+    ///std::list<LpSolverBase::Col>
+    ///\endcode
+    ///- a standard STL compatible iterable container with
+    ///\ref Col as its \c mapped_type
+    ///like
+    ///\code
+    ///std::map<AnyType,LpSolverBase::Col>
+    ///\endcode
+    ///- an iterable lemon \ref concepts::WriteMap "write map" like
+    ///\code
+    ///ListGraph::NodeMap<LpSolverBase::Col>
+    ///ListGraph::EdgeMap<LpSolverBase::Col>
+    ///\endcode
+    ///\return The number of the created column.
+#ifdef DOXYGEN
+    template<class T>
+    int addColSet(T &t) { return 0;}
+#else
+    template<class T>
+    typename enable_if<typename T::value_type::LpSolverCol,int>::type
+    addColSet(T &t,dummy<0> = 0) {
+      int s=0;
+      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addCol();s++;}
+      return s;
+    }
+    template<class T>
+    typename enable_if<typename T::value_type::second_type::LpSolverCol,
+                       int>::type
+    addColSet(T &t,dummy<1> = 1) {
+      int s=0;
+      for(typename T::iterator i=t.begin();i!=t.end();++i) {
+        i->second=addCol();
+        s++;
+      }
+      return s;
+    }
+    template<class T>
+    typename enable_if<typename T::MapIt::Value::LpSolverCol,
+                       int>::type
+    addColSet(T &t,dummy<2> = 2) {
+      int s=0;
+      for(typename T::MapIt i(t); i!=INVALID; ++i)
+        {
+          i.set(addCol());
+          s++;
+        }
+      return s;
+    }
+#endif
+
+    ///Set a column (i.e a dual constraint) of the LP
+
+    ///\param c is the column to be modified
+    ///\param e is a dual linear expression (see \ref DualExpr)
+    ///a better one.
+    void col(Col c,const DualExpr &e) {
+      e.simplify();
+      _setColCoeffs(_lpId(c), ConstColIterator(e.begin(), *this),
+                    ConstColIterator(e.end(), *this));
+    }
+
+    ///Get a column (i.e a dual constraint) of the LP
+
+    ///\param r is the column to get
+    ///\return the dual expression associated to the column
+    DualExpr col(Col c) const {
+      DualExpr e;
+      _getColCoeffs(_lpId(c), ColIterator(std::inserter(e, e.end()), *this));
+      return e;
+    }
+
+    ///Add a new column to the LP
+
+    ///\param e is a dual linear expression (see \ref DualExpr)
+    ///\param obj is the corresponding component of the objective
+    ///function. It is 0 by default.
+    ///\return The created column.
+    Col addCol(const DualExpr &e, Value o = 0) {
+      Col c=addCol();
+      col(c,e);
+      objCoeff(c,o);
+      return c;
+    }
+
+    ///Add a new empty row (i.e a new constraint) to the LP
+
+    ///This function adds a new empty row (i.e a new constraint) to the LP.
+    ///\return The created row
+    Row addRow() { Row r; _addRow(); r.id = rows.addId(); return r;}
+
+    ///\brief Add several new rows
+    ///(i.e a constraints) at once
+    ///
+    ///This magic function takes a container as its argument
+    ///and fills its elements
+    ///with new row (i.e. variables)
+    ///\param t can be
+    ///- a standard STL compatible iterable container with
+    ///\ref Row as its \c values_type
+    ///like
+    ///\code
+    ///std::vector<LpSolverBase::Row>
+    ///std::list<LpSolverBase::Row>
+    ///\endcode
+    ///- a standard STL compatible iterable container with
+    ///\ref Row as its \c mapped_type
+    ///like
+    ///\code
+    ///std::map<AnyType,LpSolverBase::Row>
+    ///\endcode
+    ///- an iterable lemon \ref concepts::WriteMap "write map" like
+    ///\code
+    ///ListGraph::NodeMap<LpSolverBase::Row>
+    ///ListGraph::EdgeMap<LpSolverBase::Row>
+    ///\endcode
+    ///\return The number of rows created.
+#ifdef DOXYGEN
+    template<class T>
+    int addRowSet(T &t) { return 0;}
+#else
+    template<class T>
+    typename enable_if<typename T::value_type::LpSolverRow,int>::type
+    addRowSet(T &t,dummy<0> = 0) {
+      int s=0;
+      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addRow();s++;}
+      return s;
+    }
+    template<class T>
+    typename enable_if<typename T::value_type::second_type::LpSolverRow,
+                       int>::type
+    addRowSet(T &t,dummy<1> = 1) {
+      int s=0;
+      for(typename T::iterator i=t.begin();i!=t.end();++i) {
+        i->second=addRow();
+        s++;
+      }
+      return s;
+    }
+    template<class T>
+    typename enable_if<typename T::MapIt::Value::LpSolverRow,
+                       int>::type
+    addRowSet(T &t,dummy<2> = 2) {
+      int s=0;
+      for(typename T::MapIt i(t); i!=INVALID; ++i)
+        {
+          i.set(addRow());
+          s++;
+        }
+      return s;
+    }
+#endif
+
+    ///Set a row (i.e a constraint) of the LP
+
+    ///\param r is the row to be modified
+    ///\param l is lower bound (-\ref INF means no bound)
+    ///\param e is a linear expression (see \ref Expr)
+    ///\param u is the upper bound (\ref INF means no bound)
+    ///\bug This is a temporary function. The interface will change to
+    ///a better one.
+    ///\todo Option to control whether a constraint with a single variable is
+    ///added or not.
+    void row(Row r, Value l, const Expr &e, Value u) {
+      e.simplify();
+      _setRowCoeffs(_lpId(r), ConstRowIterator(e.begin(), *this),
+                    ConstRowIterator(e.end(), *this));
+      _setRowBounds(_lpId(r),l-e.constComp(),u-e.constComp());
+    }
+
+    ///Set a row (i.e a constraint) of the LP
+
+    ///\param r is the row to be modified
+    ///\param c is a linear expression (see \ref Constr)
+    void row(Row r, const Constr &c) {
+      row(r, c.lowerBounded()?c.lowerBound():-INF,
+          c.expr(), c.upperBounded()?c.upperBound():INF);
+    }
+
+
+    ///Get a row (i.e a constraint) of the LP
+
+    ///\param r is the row to get
+    ///\return the expression associated to the row
+    Expr row(Row r) const {
+      Expr e;
+      _getRowCoeffs(_lpId(r), RowIterator(std::inserter(e, e.end()), *this));
+      return e;
+    }
+
+    ///Add a new row (i.e a new constraint) to the LP
+
+    ///\param l is the lower bound (-\ref INF means no bound)
+    ///\param e is a linear expression (see \ref Expr)
+    ///\param u is the upper bound (\ref INF means no bound)
+    ///\return The created row.
+    ///\bug This is a temporary function. The interface will change to
+    ///a better one.
+    Row addRow(Value l,const Expr &e, Value u) {
+      Row r=addRow();
+      row(r,l,e,u);
+      return r;
+    }
+
+    ///Add a new row (i.e a new constraint) to the LP
+
+    ///\param c is a linear expression (see \ref Constr)
+    ///\return The created row.
+    Row addRow(const Constr &c) {
+      Row r=addRow();
+      row(r,c);
+      return r;
+    }
+    ///Erase a coloumn (i.e a variable) from the LP
+
+    ///\param c is the coloumn to be deleted
+    ///\todo Please check this
+    void eraseCol(Col c) {
+      _eraseCol(_lpId(c));
+      cols.eraseId(c.id);
+    }
+    ///Erase a  row (i.e a constraint) from the LP
+
+    ///\param r is the row to be deleted
+    ///\todo Please check this
+    void eraseRow(Row r) {
+      _eraseRow(_lpId(r));
+      rows.eraseId(r.id);
+    }
+
+    /// Get the name of a column
+
+    ///\param c is the coresponding coloumn
+    ///\return The name of the colunm
+    std::string colName(Col c) const {
+      std::string name;
+      _getColName(_lpId(c), name);
+      return name;
+    }
+
+    /// Set the name of a column
+
+    ///\param c is the coresponding coloumn
+    ///\param name The name to be given
+    void colName(Col c, const std::string& name) {
+      _setColName(_lpId(c), name);
+    }
+
+    /// Get the column by its name
+
+    ///\param name The name of the column
+    ///\return the proper column or \c INVALID
+    Col colByName(const std::string& name) const {
+      int k = _colByName(name);
+      return k != -1 ? Col(cols.fixId(k)) : Col(INVALID);
+    }
+
+    /// Set an element of the coefficient matrix of the LP
+
+    ///\param r is the row of the element to be modified
+    ///\param c is the coloumn of the element to be modified
+    ///\param val is the new value of the coefficient
+
+    void coeff(Row r, Col c, Value val) {
+      _setCoeff(_lpId(r),_lpId(c), val);
+    }
+
+    /// Get an element of the coefficient matrix of the LP
+
+    ///\param r is the row of the element in question
+    ///\param c is the coloumn of the element in question
+    ///\return the corresponding coefficient
+
+    Value coeff(Row r, Col c) const {
+      return _getCoeff(_lpId(r),_lpId(c));
+    }
+
+    /// Set the lower bound of a column (i.e a variable)
+
+    /// The lower bound of a variable (column) has to be given by an
+    /// extended number of type Value, i.e. a finite number of type
+    /// Value or -\ref INF.
+    void colLowerBound(Col c, Value value) {
+      _setColLowerBound(_lpId(c),value);
+    }
+
+    /// Get the lower bound of a column (i.e a variable)
+
+    /// This function returns the lower bound for column (variable) \t c
+    /// (this might be -\ref INF as well).
+    ///\return The lower bound for coloumn \t c
+    Value colLowerBound(Col c) const {
+      return _getColLowerBound(_lpId(c));
+    }
+
+    ///\brief Set the lower bound of  several columns
+    ///(i.e a variables) at once
+    ///
+    ///This magic function takes a container as its argument
+    ///and applies the function on all of its elements.
+    /// The lower bound of a variable (column) has to be given by an
+    /// extended number of type Value, i.e. a finite number of type
+    /// Value or -\ref INF.
+#ifdef DOXYGEN
+    template<class T>
+    void colLowerBound(T &t, Value value) { return 0;}
+#else
+    template<class T>
+    typename enable_if<typename T::value_type::LpSolverCol,void>::type
+    colLowerBound(T &t, Value value,dummy<0> = 0) {
+      for(typename T::iterator i=t.begin();i!=t.end();++i) {
+        colLowerBound(*i, value);
+      }
+    }
+    template<class T>
+    typename enable_if<typename T::value_type::second_type::LpSolverCol,
+                       void>::type
+    colLowerBound(T &t, Value value,dummy<1> = 1) {
+      for(typename T::iterator i=t.begin();i!=t.end();++i) {
+        colLowerBound(i->second, value);
+      }
+    }
+    template<class T>
+    typename enable_if<typename T::MapIt::Value::LpSolverCol,
+                       void>::type
+    colLowerBound(T &t, Value value,dummy<2> = 2) {
+      for(typename T::MapIt i(t); i!=INVALID; ++i){
+        colLowerBound(*i, value);
+      }
+    }
+#endif
+
+    /// Set the upper bound of a column (i.e a variable)
+
+    /// The upper bound of a variable (column) has to be given by an
+    /// extended number of type Value, i.e. a finite number of type
+    /// Value or \ref INF.
+    void colUpperBound(Col c, Value value) {
+      _setColUpperBound(_lpId(c),value);
+    };
+
+    /// Get the upper bound of a column (i.e a variable)
+
+    /// This function returns the upper bound for column (variable) \t c
+    /// (this might be \ref INF as well).
+    ///\return The upper bound for coloumn \t c
+    Value colUpperBound(Col c) const {
+      return _getColUpperBound(_lpId(c));
+    }
+
+    ///\brief Set the upper bound of  several columns
+    ///(i.e a variables) at once
+    ///
+    ///This magic function takes a container as its argument
+    ///and applies the function on all of its elements.
+    /// The upper bound of a variable (column) has to be given by an
+    /// extended number of type Value, i.e. a finite number of type
+    /// Value or \ref INF.
+#ifdef DOXYGEN
+    template<class T>
+    void colUpperBound(T &t, Value value) { return 0;}
+#else
+    template<class T>
+    typename enable_if<typename T::value_type::LpSolverCol,void>::type
+    colUpperBound(T &t, Value value,dummy<0> = 0) {
+      for(typename T::iterator i=t.begin();i!=t.end();++i) {
+        colUpperBound(*i, value);
+      }
+    }
+    template<class T>
+    typename enable_if<typename T::value_type::second_type::LpSolverCol,
+                       void>::type
+    colUpperBound(T &t, Value value,dummy<1> = 1) {
+      for(typename T::iterator i=t.begin();i!=t.end();++i) {
+        colUpperBound(i->second, value);
+      }
+    }
+    template<class T>
+    typename enable_if<typename T::MapIt::Value::LpSolverCol,
+                       void>::type
+    colUpperBound(T &t, Value value,dummy<2> = 2) {
+      for(typename T::MapIt i(t); i!=INVALID; ++i){
+        colUpperBound(*i, value);
+      }
+    }
+#endif
+
+    /// Set the lower and the upper bounds of a column (i.e a variable)
+
+    /// The lower and the upper bounds of
+    /// a variable (column) have to be given by an
+    /// extended number of type Value, i.e. a finite number of type
+    /// Value, -\ref INF or \ref INF.
+    void colBounds(Col c, Value lower, Value upper) {
+      _setColLowerBound(_lpId(c),lower);
+      _setColUpperBound(_lpId(c),upper);
+    }
+
+    ///\brief Set the lower and the upper bound of several columns
+    ///(i.e a variables) at once
+    ///
+    ///This magic function takes a container as its argument
+    ///and applies the function on all of its elements.
+    /// The lower and the upper bounds of
+    /// a variable (column) have to be given by an
+    /// extended number of type Value, i.e. a finite number of type
+    /// Value, -\ref INF or \ref INF.
+#ifdef DOXYGEN
+    template<class T>
+    void colBounds(T &t, Value lower, Value upper) { return 0;}
+#else
+    template<class T>
+    typename enable_if<typename T::value_type::LpSolverCol,void>::type
+    colBounds(T &t, Value lower, Value upper,dummy<0> = 0) {
+      for(typename T::iterator i=t.begin();i!=t.end();++i) {
+        colBounds(*i, lower, upper);
+      }
+    }
+    template<class T>
+    typename enable_if<typename T::value_type::second_type::LpSolverCol,
+                       void>::type
+    colBounds(T &t, Value lower, Value upper,dummy<1> = 1) {
+      for(typename T::iterator i=t.begin();i!=t.end();++i) {
+        colBounds(i->second, lower, upper);
+      }
+    }
+    template<class T>
+    typename enable_if<typename T::MapIt::Value::LpSolverCol,
+                       void>::type
+    colBounds(T &t, Value lower, Value upper,dummy<2> = 2) {
+      for(typename T::MapIt i(t); i!=INVALID; ++i){
+        colBounds(*i, lower, upper);
+      }
+    }
+#endif
+
+
+    /// Set the lower and the upper bounds of a row (i.e a constraint)
+
+    /// The lower and the upper bound of a constraint (row) have to be
+    /// given by an extended number of type Value, i.e. a finite
+    /// number of type Value, -\ref INF or \ref INF. There is no
+    /// separate function for the lower and the upper bound because
+    /// that would have been hard to implement for CPLEX.
+    void rowBounds(Row c, Value lower, Value upper) {
+      _setRowBounds(_lpId(c),lower, upper);
+    }
+
+    /// Get the lower and the upper bounds of a row (i.e a constraint)
+
+    /// The lower and the upper bound of
+    /// a constraint (row) are
+    /// extended numbers of type Value, i.e.  finite numbers of type
+    /// Value, -\ref INF or \ref INF.
+    /// \todo There is no separate function for the
+    /// lower and the upper bound because we had problems with the
+    /// implementation of the setting functions for CPLEX:
+    /// check out whether this can be done for these functions.
+    void getRowBounds(Row c, Value &lower, Value &upper) const {
+      _getRowBounds(_lpId(c),lower, upper);
+    }
+
+    ///Set an element of the objective function
+    void objCoeff(Col c, Value v) {_setObjCoeff(_lpId(c),v); };
+
+    ///Get an element of the objective function
+    Value objCoeff(Col c) const { return _getObjCoeff(_lpId(c)); };
+
+    ///Set the objective function
+
+    ///\param e is a linear expression of type \ref Expr.
+    void obj(Expr e) {
+      _clearObj();
+      for (Expr::iterator i=e.begin(); i!=e.end(); ++i)
+        objCoeff((*i).first,(*i).second);
+      obj_const_comp=e.constComp();
+    }
+
+    ///Get the objective function
+
+    ///\return the objective function as a linear expression of type \ref Expr.
+    Expr obj() const {
+      Expr e;
+      for (ColIt it(*this); it != INVALID; ++it) {
+        double c = objCoeff(it);
+        if (c != 0.0) {
+          e.insert(std::make_pair(it, c));
+        }
+      }
+      return e;
+    }
+
+
+    ///Maximize
+    void max() { _setMax(); }
+    ///Minimize
+    void min() { _setMin(); }
+
+    ///Query function: is this a maximization problem?
+    bool isMax() const {return _isMax(); }
+
+    ///Query function: is this a minimization problem?
+    bool isMin() const {return !isMax(); }
+
+    ///@}
+
+
+    ///\name Solve the LP
+
+    ///@{
+
+    ///\e Solve the LP problem at hand
+    ///
+    ///\return The result of the optimization procedure. Possible
+    ///values and their meanings can be found in the documentation of
+    ///\ref SolveExitStatus.
+    ///
+    ///\todo Which method is used to solve the problem
+    SolveExitStatus solve() { return _solve(); }
+
+    ///@}
+
+    ///\name Obtain the solution
+
+    ///@{
+
+    /// The status of the primal problem (the original LP problem)
+    SolutionStatus primalStatus() const {
+      return _getPrimalStatus();
+    }
+
+    /// The status of the dual (of the original LP) problem
+    SolutionStatus dualStatus() const {
+      return _getDualStatus();
+    }
+
+    ///The type of the original LP problem
+    ProblemTypes problemType() const {
+      return _getProblemType();
+    }
+
+    ///\e
+    Value primal(Col c) const { return _getPrimal(_lpId(c)); }
+    ///\e
+    Value primal(const Expr& e) const {
+      double res = e.constComp();
+      for (std::map<Col, double>::const_iterator it = e.begin();
+           it != e.end(); ++it) {
+        res += _getPrimal(_lpId(it->first)) * it->second;
+      }
+      return res;
+    }
+
+    ///\e
+    Value dual(Row r) const { return _getDual(_lpId(r)); }
+    ///\e
+    Value dual(const DualExpr& e) const {
+      double res = 0.0;
+      for (std::map<Row, double>::const_iterator it = e.begin();
+           it != e.end(); ++it) {
+        res += _getPrimal(_lpId(it->first)) * it->second;
+      }
+      return res;
+    }
+
+    ///\e
+    bool isBasicCol(Col c) const { return _isBasicCol(_lpId(c)); }
+
+    ///\e
+
+    ///\return
+    ///- \ref INF or -\ref INF means either infeasibility or unboundedness
+    /// of the primal problem, depending on whether we minimize or maximize.
+    ///- \ref NaN if no primal solution is found.
+    ///- The (finite) objective value if an optimal solution is found.
+    Value primalValue() const { return _getPrimalValue()+obj_const_comp;}
+    ///@}
+
+  };
+
+
+  /// \ingroup lp_group
+  ///
+  /// \brief Common base class for MIP solvers
+  /// \todo Much more docs
+  class MipSolverBase : virtual public LpSolverBase{
+  public:
+
+    ///Possible variable (coloumn) types (e.g. real, integer, binary etc.)
+    enum ColTypes {
+      ///Continuous variable
+      REAL = 0,
+      ///Integer variable
+
+      ///Unfortunately, cplex 7.5 somewhere writes something like
+      ///#define INTEGER 'I'
+      INT = 1
+      ///\todo No support for other types yet.
+    };
+
+    ///Sets the type of the given coloumn to the given type
+    ///
+    ///Sets the type of the given coloumn to the given type.
+    void colType(Col c, ColTypes col_type) {
+      _colType(_lpId(c),col_type);
+    }
+
+    ///Gives back the type of the column.
+    ///
+    ///Gives back the type of the column.
+    ColTypes colType(Col c) const {
+      return _colType(_lpId(c));
+    }
+
+    ///Sets the type of the given Col to integer or remove that property.
+    ///
+    ///Sets the type of the given Col to integer or remove that property.
+    void integer(Col c, bool enable) {
+      if (enable)
+        colType(c,INT);
+      else
+        colType(c,REAL);
+    }
+
+    ///Gives back whether the type of the column is integer or not.
+    ///
+    ///Gives back the type of the column.
+    ///\return true if the column has integer type and false if not.
+    bool integer(Col c) const {
+      return (colType(c)==INT);
+    }
+
+    /// The status of the MIP problem
+    SolutionStatus mipStatus() const {
+      return _getMipStatus();
+    }
+
+  protected:
+
+    virtual ColTypes _colType(int col) const = 0;
+    virtual void _colType(int col, ColTypes col_type) = 0;
+    virtual SolutionStatus _getMipStatus() const = 0;
+
+  };
+
+  ///\relates LpSolverBase::Expr
+  ///
+  inline LpSolverBase::Expr operator+(const LpSolverBase::Expr &a,
+                                      const LpSolverBase::Expr &b)
+  {
+    LpSolverBase::Expr tmp(a);
+    tmp+=b;
+    return tmp;
+  }
+  ///\e
+
+  ///\relates LpSolverBase::Expr
+  ///
+  inline LpSolverBase::Expr operator-(const LpSolverBase::Expr &a,
+                                      const LpSolverBase::Expr &b)
+  {
+    LpSolverBase::Expr tmp(a);
+    tmp-=b;
+    return tmp;
+  }
+  ///\e
+
+  ///\relates LpSolverBase::Expr
+  ///
+  inline LpSolverBase::Expr operator*(const LpSolverBase::Expr &a,
+                                      const LpSolverBase::Value &b)
+  {
+    LpSolverBase::Expr tmp(a);
+    tmp*=b;
+    return tmp;
+  }
+
+  ///\e
+
+  ///\relates LpSolverBase::Expr
+  ///
+  inline LpSolverBase::Expr operator*(const LpSolverBase::Value &a,
+                                      const LpSolverBase::Expr &b)
+  {
+    LpSolverBase::Expr tmp(b);
+    tmp*=a;
+    return tmp;
+  }
+  ///\e
+
+  ///\relates LpSolverBase::Expr
+  ///
+  inline LpSolverBase::Expr operator/(const LpSolverBase::Expr &a,
+                                      const LpSolverBase::Value &b)
+  {
+    LpSolverBase::Expr tmp(a);
+    tmp/=b;
+    return tmp;
+  }
+
+  ///\e
+
+  ///\relates LpSolverBase::Constr
+  ///
+  inline LpSolverBase::Constr operator<=(const LpSolverBase::Expr &e,
+                                         const LpSolverBase::Expr &f)
+  {
+    return LpSolverBase::Constr(-LpSolverBase::INF,e-f,0);
+  }
+
+  ///\e
+
+  ///\relates LpSolverBase::Constr
+  ///
+  inline LpSolverBase::Constr operator<=(const LpSolverBase::Value &e,
+                                         const LpSolverBase::Expr &f)
+  {
+    return LpSolverBase::Constr(e,f);
+  }
+
+  ///\e
+
+  ///\relates LpSolverBase::Constr
+  ///
+  inline LpSolverBase::Constr operator<=(const LpSolverBase::Expr &e,
+                                         const LpSolverBase::Value &f)
+  {
+    return LpSolverBase::Constr(-LpSolverBase::INF,e,f);
+  }
+
+  ///\e
+
+  ///\relates LpSolverBase::Constr
+  ///
+  inline LpSolverBase::Constr operator>=(const LpSolverBase::Expr &e,
+                                         const LpSolverBase::Expr &f)
+  {
+    return LpSolverBase::Constr(-LpSolverBase::INF,f-e,0);
+  }
+
+
+  ///\e
+
+  ///\relates LpSolverBase::Constr
+  ///
+  inline LpSolverBase::Constr operator>=(const LpSolverBase::Value &e,
+                                         const LpSolverBase::Expr &f)
+  {
+    return LpSolverBase::Constr(f,e);
+  }
+
+
+  ///\e
+
+  ///\relates LpSolverBase::Constr
+  ///
+  inline LpSolverBase::Constr operator>=(const LpSolverBase::Expr &e,
+                                         const LpSolverBase::Value &f)
+  {
+    return LpSolverBase::Constr(f,e,LpSolverBase::INF);
+  }
+
+  ///\e
+
+  ///\relates LpSolverBase::Constr
+  ///
+  inline LpSolverBase::Constr operator==(const LpSolverBase::Expr &e,
+                                         const LpSolverBase::Value &f)
+  {
+    return LpSolverBase::Constr(f,e,f);
+  }
+
+  ///\e
+
+  ///\relates LpSolverBase::Constr
+  ///
+  inline LpSolverBase::Constr operator==(const LpSolverBase::Expr &e,
+                                         const LpSolverBase::Expr &f)
+  {
+    return LpSolverBase::Constr(0,e-f,0);
+  }
+
+  ///\e
+
+  ///\relates LpSolverBase::Constr
+  ///
+  inline LpSolverBase::Constr operator<=(const LpSolverBase::Value &n,
+                                         const LpSolverBase::Constr&c)
+  {
+    LpSolverBase::Constr tmp(c);
+    LEMON_ASSERT(LpSolverBase::isNaN(tmp.lowerBound()), "Wrong LP constraint");
+    tmp.lowerBound()=n;
+    return tmp;
+  }
+  ///\e
+
+  ///\relates LpSolverBase::Constr
+  ///
+  inline LpSolverBase::Constr operator<=(const LpSolverBase::Constr& c,
+                                         const LpSolverBase::Value &n)
+  {
+    LpSolverBase::Constr tmp(c);
+    LEMON_ASSERT(LpSolverBase::isNaN(tmp.upperBound()), "Wrong LP constraint");
+    tmp.upperBound()=n;
+    return tmp;
+  }
+
+  ///\e
+
+  ///\relates LpSolverBase::Constr
+  ///
+  inline LpSolverBase::Constr operator>=(const LpSolverBase::Value &n,
+                                         const LpSolverBase::Constr&c)
+  {
+    LpSolverBase::Constr tmp(c);
+    LEMON_ASSERT(LpSolverBase::isNaN(tmp.upperBound()), "Wrong LP constraint");
+    tmp.upperBound()=n;
+    return tmp;
+  }
+  ///\e
+
+  ///\relates LpSolverBase::Constr
+  ///
+  inline LpSolverBase::Constr operator>=(const LpSolverBase::Constr& c,
+                                         const LpSolverBase::Value &n)
+  {
+    LpSolverBase::Constr tmp(c);
+    LEMON_ASSERT(LpSolverBase::isNaN(tmp.lowerBound()), "Wrong LP constraint");
+    tmp.lowerBound()=n;
+    return tmp;
+  }
+
+  ///\e
+
+  ///\relates LpSolverBase::DualExpr
+  ///
+  inline LpSolverBase::DualExpr operator+(const LpSolverBase::DualExpr &a,
+                                          const LpSolverBase::DualExpr &b)
+  {
+    LpSolverBase::DualExpr tmp(a);
+    tmp+=b;
+    return tmp;
+  }
+  ///\e
+
+  ///\relates LpSolverBase::DualExpr
+  ///
+  inline LpSolverBase::DualExpr operator-(const LpSolverBase::DualExpr &a,
+                                          const LpSolverBase::DualExpr &b)
+  {
+    LpSolverBase::DualExpr tmp(a);
+    tmp-=b;
+    return tmp;
+  }
+  ///\e
+
+  ///\relates LpSolverBase::DualExpr
+  ///
+  inline LpSolverBase::DualExpr operator*(const LpSolverBase::DualExpr &a,
+                                          const LpSolverBase::Value &b)
+  {
+    LpSolverBase::DualExpr tmp(a);
+    tmp*=b;
+    return tmp;
+  }
+
+  ///\e
+
+  ///\relates LpSolverBase::DualExpr
+  ///
+  inline LpSolverBase::DualExpr operator*(const LpSolverBase::Value &a,
+                                          const LpSolverBase::DualExpr &b)
+  {
+    LpSolverBase::DualExpr tmp(b);
+    tmp*=a;
+    return tmp;
+  }
+  ///\e
+
+  ///\relates LpSolverBase::DualExpr
+  ///
+  inline LpSolverBase::DualExpr operator/(const LpSolverBase::DualExpr &a,
+                                          const LpSolverBase::Value &b)
+  {
+    LpSolverBase::DualExpr tmp(a);
+    tmp/=b;
+    return tmp;
+  }
+
+
+} //namespace lemon
+
+#endif //LEMON_LP_BASE_H