# HG changeset patch
# User Peter Kovacs <kpeter@inf.elte.hu>
# Date 1266193485 -3600
# Node ID 7d70e97356868cf1953c9060a3112ef83e7fb3fa
# Parent  bc3ef6652f1bffa5e9d3661ad9a92c43b0cb1a45
Add a preliminary page about the LP interface

diff -r bc3ef6652f1b -r 7d70e9735686 lp.dox
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lp.dox	Mon Feb 15 01:24:45 2010 +0100
@@ -0,0 +1,103 @@
+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library.
+ *
+ * Copyright (C) 2003-2009
+ * 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.
+ *
+ */
+
+namespace lemon {
+/**
+[PAGE]sec_lp[PAGE] Linear Programming Interface
+
+\todo Clarify this section.
+
+Linear programming (LP) is one of the most important
+general methods of operations research and LP solvers are widely used in
+optimization software. The interface provided in LEMON makes it possible to
+specify LP problems using a high-level syntax.
+
+\code
+  Lp lp;
+
+  Lp::Col x1 = lp.addCol();
+  Lp::Col x2 = lp.addCol();
+
+  lp.addRow(0 <= x1 + x2 <= 100);
+  lp.addRow(2 * x1 <= x2 + 32);
+
+  lp.colLowerBound(x1, 0);
+  lp.colUpperBound(x2, 100);
+
+  lp.max();
+  lp.obj(10 * x1 + 6 * x2);
+  lp.solve();
+
+  cout << "Objective function value: " << lp.primal() << endl;
+  cout << "x1 = " << lp.primal(x1) << endl;
+  cout << "x2 = " << lp.primal(x2) << endl;
+\endcode
+
+\ref LpBase::Col "Lp::Col" type represents the variables in the LP problems,
+while \ref LpBase::Row "Lp::Row" represents the constraints. The numerical
+operators can be used to form expressions from columns and dual
+expressions from rows. Due to the suitable operator overloads,
+a problem can be described in C++ conveniently, directly as it is
+expressed in mathematics.
+
+
+The following example solves a maximum flow problem with linear
+programming. Several other graph optimization problems can also be
+expressed as linear programs and this interface helps to solve them easily
+(though usually not so efficiently as by a direct combinatorial method).
+
+\code
+  Lp lp;
+  Digraph::ArcMap<Lp::Col> f(g);
+  lp.addColSet(f);
+
+  // Capacity constraints
+  for (Digraph::ArcIt a(g); a != INVALID; ++a) {
+    lp.colLowerBound(f[a], 0);
+    lp.colUpperBound(f[a], capacity[a]);
+  }
+
+  // Flow conservation constraints
+  for (Digraph::NodeIt n(g); n != INVALID; ++n) {
+    if (n == src || n == trg) continue;
+    Lp::Expr e;
+    for (Digraph::OutArcIt a(g,n); a != INVALID; ++a) e += f[a];
+    for (Digraph::InArcIt a(g,n); a != INVALID; ++a) e -= f[a];
+    lp.addRow(e == 0);
+  }
+
+  // Objective function
+  Lp::Expr o;
+  for (Digraph::OutArcIt a(g,src); a != INVALID; ++a) o += f[a];
+  for (Digraph::InArcIt a(g,src); a != INVALID; ++a) o -= f[a];
+
+  lp.max();
+  lp.obj(o);
+  lp.solve();
+\endcode
+
+Note that LEMON does not implement an LP solver, it just wraps various
+libraries with a uniform high-level interface.
+Currently, the following linear and mixed integer programming packages are
+supported: GLPK, Clp, Cbc, ILOG CPLEX and SoPlex.
+However, additional wrapper classes for new solvers can also be implemented
+quite easily.
+
+[TRAILER]
+*/
+}
\ No newline at end of file
diff -r bc3ef6652f1b -r 7d70e9735686 toc.txt
--- a/toc.txt	Mon Feb 15 01:18:18 2010 +0100
+++ b/toc.txt	Mon Feb 15 01:24:45 2010 +0100
@@ -17,8 +17,9 @@
 ** sec_undir_graphs
 ** sec_special_graphs
 * sec_graph_adaptors
+* sec_lp
+*_sec_lgf
 *_sec_tools
-**_sec_lgf
 **_sec_time_count
 **_sec_random
 **_sec_graph_to_eps