alpar@1: /* glpapi08.c (interior-point method routines) */
alpar@1: 
alpar@1: /***********************************************************************
alpar@1: *  This code is part of GLPK (GNU Linear Programming Kit).
alpar@1: *
alpar@1: *  Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008,
alpar@1: *  2009, 2010 Andrew Makhorin, Department for Applied Informatics,
alpar@1: *  Moscow Aviation Institute, Moscow, Russia. All rights reserved.
alpar@1: *  E-mail: <mao@gnu.org>.
alpar@1: *
alpar@1: *  GLPK is free software: you can redistribute it and/or modify it
alpar@1: *  under the terms of the GNU General Public License as published by
alpar@1: *  the Free Software Foundation, either version 3 of the License, or
alpar@1: *  (at your option) any later version.
alpar@1: *
alpar@1: *  GLPK is distributed in the hope that it will be useful, but WITHOUT
alpar@1: *  ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
alpar@1: *  or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
alpar@1: *  License for more details.
alpar@1: *
alpar@1: *  You should have received a copy of the GNU General Public License
alpar@1: *  along with GLPK. If not, see <http://www.gnu.org/licenses/>.
alpar@1: ***********************************************************************/
alpar@1: 
alpar@1: #include "glpapi.h"
alpar@1: #include "glpipm.h"
alpar@1: #include "glpnpp.h"
alpar@1: 
alpar@1: /***********************************************************************
alpar@1: *  NAME
alpar@1: *
alpar@1: *  glp_interior - solve LP problem with the interior-point method
alpar@1: *
alpar@1: *  SYNOPSIS
alpar@1: *
alpar@1: *  int glp_interior(glp_prob *P, const glp_iptcp *parm);
alpar@1: *
alpar@1: *  The routine glp_interior is a driver to the LP solver based on the
alpar@1: *  interior-point method.
alpar@1: *
alpar@1: *  The interior-point solver has a set of control parameters. Values of
alpar@1: *  the control parameters can be passed in a structure glp_iptcp, which
alpar@1: *  the parameter parm points to.
alpar@1: *
alpar@1: *  Currently this routine implements an easy variant of the primal-dual
alpar@1: *  interior-point method based on Mehrotra's technique.
alpar@1: *
alpar@1: *  This routine transforms the original LP problem to an equivalent LP
alpar@1: *  problem in the standard formulation (all constraints are equalities,
alpar@1: *  all variables are non-negative), calls the routine ipm_main to solve
alpar@1: *  the transformed problem, and then transforms an obtained solution to
alpar@1: *  the solution of the original problem.
alpar@1: *
alpar@1: *  RETURNS
alpar@1: *
alpar@1: *  0  The LP problem instance has been successfully solved. This code
alpar@1: *     does not necessarily mean that the solver has found optimal
alpar@1: *     solution. It only means that the solution process was successful.
alpar@1: *
alpar@1: *  GLP_EFAIL
alpar@1: *     The problem has no rows/columns.
alpar@1: *
alpar@1: *  GLP_ENOCVG
alpar@1: *     Very slow convergence or divergence.
alpar@1: *
alpar@1: *  GLP_EITLIM
alpar@1: *     Iteration limit exceeded.
alpar@1: *
alpar@1: *  GLP_EINSTAB
alpar@1: *     Numerical instability on solving Newtonian system. */
alpar@1: 
alpar@1: static void transform(NPP *npp)
alpar@1: {     /* transform LP to the standard formulation */
alpar@1:       NPPROW *row, *prev_row;
alpar@1:       NPPCOL *col, *prev_col;
alpar@1:       for (row = npp->r_tail; row != NULL; row = prev_row)
alpar@1:       {  prev_row = row->prev;
alpar@1:          if (row->lb == -DBL_MAX && row->ub == +DBL_MAX)
alpar@1:             npp_free_row(npp, row);
alpar@1:          else if (row->lb == -DBL_MAX)
alpar@1:             npp_leq_row(npp, row);
alpar@1:          else if (row->ub == +DBL_MAX)
alpar@1:             npp_geq_row(npp, row);
alpar@1:          else if (row->lb != row->ub)
alpar@1:          {  if (fabs(row->lb) < fabs(row->ub))
alpar@1:                npp_geq_row(npp, row);
alpar@1:             else
alpar@1:                npp_leq_row(npp, row);
alpar@1:          }
alpar@1:       }
alpar@1:       for (col = npp->c_tail; col != NULL; col = prev_col)
alpar@1:       {  prev_col = col->prev;
alpar@1:          if (col->lb == -DBL_MAX && col->ub == +DBL_MAX)
alpar@1:             npp_free_col(npp, col);
alpar@1:          else if (col->lb == -DBL_MAX)
alpar@1:             npp_ubnd_col(npp, col);
alpar@1:          else if (col->ub == +DBL_MAX)
alpar@1:          {  if (col->lb != 0.0)
alpar@1:                npp_lbnd_col(npp, col);
alpar@1:          }
alpar@1:          else if (col->lb != col->ub)
alpar@1:          {  if (fabs(col->lb) < fabs(col->ub))
alpar@1:             {  if (col->lb != 0.0)
alpar@1:                   npp_lbnd_col(npp, col);
alpar@1:             }
alpar@1:             else
alpar@1:                npp_ubnd_col(npp, col);
alpar@1:             npp_dbnd_col(npp, col);
alpar@1:          }
alpar@1:          else
alpar@1:             npp_fixed_col(npp, col);
alpar@1:       }
alpar@1:       for (row = npp->r_head; row != NULL; row = row->next)
alpar@1:          xassert(row->lb == row->ub);
alpar@1:       for (col = npp->c_head; col != NULL; col = col->next)
alpar@1:          xassert(col->lb == 0.0 && col->ub == +DBL_MAX);
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: int glp_interior(glp_prob *P, const glp_iptcp *parm)
alpar@1: {     glp_iptcp _parm;
alpar@1:       GLPROW *row;
alpar@1:       GLPCOL *col;
alpar@1:       NPP *npp = NULL;
alpar@1:       glp_prob *prob = NULL;
alpar@1:       int i, j, ret;
alpar@1:       /* check control parameters */
alpar@1:       if (parm == NULL)
alpar@1:          glp_init_iptcp(&_parm), parm = &_parm;
alpar@1:       if (!(parm->msg_lev == GLP_MSG_OFF ||
alpar@1:             parm->msg_lev == GLP_MSG_ERR ||
alpar@1:             parm->msg_lev == GLP_MSG_ON  ||
alpar@1:             parm->msg_lev == GLP_MSG_ALL))
alpar@1:          xerror("glp_interior: msg_lev = %d; invalid parameter\n",
alpar@1:             parm->msg_lev);
alpar@1:       if (!(parm->ord_alg == GLP_ORD_NONE ||
alpar@1:             parm->ord_alg == GLP_ORD_QMD ||
alpar@1:             parm->ord_alg == GLP_ORD_AMD ||
alpar@1:             parm->ord_alg == GLP_ORD_SYMAMD))
alpar@1:          xerror("glp_interior: ord_alg = %d; invalid parameter\n",
alpar@1:             parm->ord_alg);
alpar@1:       /* interior-point solution is currently undefined */
alpar@1:       P->ipt_stat = GLP_UNDEF;
alpar@1:       P->ipt_obj = 0.0;
alpar@1:       /* check bounds of double-bounded variables */
alpar@1:       for (i = 1; i <= P->m; i++)
alpar@1:       {  row = P->row[i];
alpar@1:          if (row->type == GLP_DB && row->lb >= row->ub)
alpar@1:          {  if (parm->msg_lev >= GLP_MSG_ERR)
alpar@1:                xprintf("glp_interior: row %d: lb = %g, ub = %g; incorre"
alpar@1:                   "ct bounds\n", i, row->lb, row->ub);
alpar@1:             ret = GLP_EBOUND;
alpar@1:             goto done;
alpar@1:          }
alpar@1:       }
alpar@1:       for (j = 1; j <= P->n; j++)
alpar@1:       {  col = P->col[j];
alpar@1:          if (col->type == GLP_DB && col->lb >= col->ub)
alpar@1:          {  if (parm->msg_lev >= GLP_MSG_ERR)
alpar@1:                xprintf("glp_interior: column %d: lb = %g, ub = %g; inco"
alpar@1:                   "rrect bounds\n", j, col->lb, col->ub);
alpar@1:             ret = GLP_EBOUND;
alpar@1:             goto done;
alpar@1:          }
alpar@1:       }
alpar@1:       /* transform LP to the standard formulation */
alpar@1:       if (parm->msg_lev >= GLP_MSG_ALL)
alpar@1:          xprintf("Original LP has %d row(s), %d column(s), and %d non-z"
alpar@1:             "ero(s)\n", P->m, P->n, P->nnz);
alpar@1:       npp = npp_create_wksp();
alpar@1:       npp_load_prob(npp, P, GLP_OFF, GLP_IPT, GLP_ON);
alpar@1:       transform(npp);
alpar@1:       prob = glp_create_prob();
alpar@1:       npp_build_prob(npp, prob);
alpar@1:       if (parm->msg_lev >= GLP_MSG_ALL)
alpar@1:          xprintf("Working LP has %d row(s), %d column(s), and %d non-ze"
alpar@1:             "ro(s)\n", prob->m, prob->n, prob->nnz);
alpar@1: #if 1
alpar@1:       /* currently empty problem cannot be solved */
alpar@1:       if (!(prob->m > 0 && prob->n > 0))
alpar@1:       {  if (parm->msg_lev >= GLP_MSG_ERR)
alpar@1:             xprintf("glp_interior: unable to solve empty problem\n");
alpar@1:          ret = GLP_EFAIL;
alpar@1:          goto done;
alpar@1:       }
alpar@1: #endif
alpar@1:       /* scale the resultant LP */
alpar@1:       {  ENV *env = get_env_ptr();
alpar@1:          int term_out = env->term_out;
alpar@1:          env->term_out = GLP_OFF;
alpar@1:          glp_scale_prob(prob, GLP_SF_EQ);
alpar@1:          env->term_out = term_out;
alpar@1:       }
alpar@1:       /* warn about dense columns */
alpar@1:       if (parm->msg_lev >= GLP_MSG_ON && prob->m >= 200)
alpar@1:       {  int len, cnt = 0;
alpar@1:          for (j = 1; j <= prob->n; j++)
alpar@1:          {  len = glp_get_mat_col(prob, j, NULL, NULL);
alpar@1:             if ((double)len >= 0.20 * (double)prob->m) cnt++;
alpar@1:          }
alpar@1:          if (cnt == 1)
alpar@1:             xprintf("WARNING: PROBLEM HAS ONE DENSE COLUMN\n");
alpar@1:          else if (cnt > 0)
alpar@1:             xprintf("WARNING: PROBLEM HAS %d DENSE COLUMNS\n", cnt);
alpar@1:       }
alpar@1:       /* solve the transformed LP */
alpar@1:       ret = ipm_solve(prob, parm);
alpar@1:       /* postprocess solution from the transformed LP */
alpar@1:       npp_postprocess(npp, prob);
alpar@1:       /* and store solution to the original LP */
alpar@1:       npp_unload_sol(npp, P);
alpar@1: done: /* free working program objects */
alpar@1:       if (npp != NULL) npp_delete_wksp(npp);
alpar@1:       if (prob != NULL) glp_delete_prob(prob);
alpar@1:       /* return to the application program */
alpar@1:       return ret;
alpar@1: }
alpar@1: 
alpar@1: /***********************************************************************
alpar@1: *  NAME
alpar@1: *
alpar@1: *  glp_init_iptcp - initialize interior-point solver control parameters
alpar@1: *
alpar@1: *  SYNOPSIS
alpar@1: *
alpar@1: *  void glp_init_iptcp(glp_iptcp *parm);
alpar@1: *
alpar@1: *  DESCRIPTION
alpar@1: *
alpar@1: *  The routine glp_init_iptcp initializes control parameters, which are
alpar@1: *  used by the interior-point solver, with default values.
alpar@1: *
alpar@1: *  Default values of the control parameters are stored in the glp_iptcp
alpar@1: *  structure, which the parameter parm points to. */
alpar@1: 
alpar@1: void glp_init_iptcp(glp_iptcp *parm)
alpar@1: {     parm->msg_lev = GLP_MSG_ALL;
alpar@1:       parm->ord_alg = GLP_ORD_AMD;
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: /***********************************************************************
alpar@1: *  NAME
alpar@1: *
alpar@1: *  glp_ipt_status - retrieve status of interior-point solution
alpar@1: *
alpar@1: *  SYNOPSIS
alpar@1: *
alpar@1: *  int glp_ipt_status(glp_prob *lp);
alpar@1: *
alpar@1: *  RETURNS
alpar@1: *
alpar@1: *  The routine glp_ipt_status reports the status of solution found by
alpar@1: *  the interior-point solver as follows:
alpar@1: *
alpar@1: *  GLP_UNDEF  - interior-point solution is undefined;
alpar@1: *  GLP_OPT    - interior-point solution is optimal;
alpar@1: *  GLP_INFEAS - interior-point solution is infeasible;
alpar@1: *  GLP_NOFEAS - no feasible solution exists. */
alpar@1: 
alpar@1: int glp_ipt_status(glp_prob *lp)
alpar@1: {     int ipt_stat = lp->ipt_stat;
alpar@1:       return ipt_stat;
alpar@1: }
alpar@1: 
alpar@1: /***********************************************************************
alpar@1: *  NAME
alpar@1: *
alpar@1: *  glp_ipt_obj_val - retrieve objective value (interior point)
alpar@1: *
alpar@1: *  SYNOPSIS
alpar@1: *
alpar@1: *  double glp_ipt_obj_val(glp_prob *lp);
alpar@1: *
alpar@1: *  RETURNS
alpar@1: *
alpar@1: *  The routine glp_ipt_obj_val returns value of the objective function
alpar@1: *  for interior-point solution. */
alpar@1: 
alpar@1: double glp_ipt_obj_val(glp_prob *lp)
alpar@1: {     /*struct LPXCPS *cps = lp->cps;*/
alpar@1:       double z;
alpar@1:       z = lp->ipt_obj;
alpar@1:       /*if (cps->round && fabs(z) < 1e-9) z = 0.0;*/
alpar@1:       return z;
alpar@1: }
alpar@1: 
alpar@1: /***********************************************************************
alpar@1: *  NAME
alpar@1: *
alpar@1: *  glp_ipt_row_prim - retrieve row primal value (interior point)
alpar@1: *
alpar@1: *  SYNOPSIS
alpar@1: *
alpar@1: *  double glp_ipt_row_prim(glp_prob *lp, int i);
alpar@1: *
alpar@1: *  RETURNS
alpar@1: *
alpar@1: *  The routine glp_ipt_row_prim returns primal value of the auxiliary
alpar@1: *  variable associated with i-th row. */
alpar@1: 
alpar@1: double glp_ipt_row_prim(glp_prob *lp, int i)
alpar@1: {     /*struct LPXCPS *cps = lp->cps;*/
alpar@1:       double pval;
alpar@1:       if (!(1 <= i && i <= lp->m))
alpar@1:          xerror("glp_ipt_row_prim: i = %d; row number out of range\n",
alpar@1:             i);
alpar@1:       pval = lp->row[i]->pval;
alpar@1:       /*if (cps->round && fabs(pval) < 1e-9) pval = 0.0;*/
alpar@1:       return pval;
alpar@1: }
alpar@1: 
alpar@1: /***********************************************************************
alpar@1: *  NAME
alpar@1: *
alpar@1: *  glp_ipt_row_dual - retrieve row dual value (interior point)
alpar@1: *
alpar@1: *  SYNOPSIS
alpar@1: *
alpar@1: *  double glp_ipt_row_dual(glp_prob *lp, int i);
alpar@1: *
alpar@1: *  RETURNS
alpar@1: *
alpar@1: *  The routine glp_ipt_row_dual returns dual value (i.e. reduced cost)
alpar@1: *  of the auxiliary variable associated with i-th row. */
alpar@1: 
alpar@1: double glp_ipt_row_dual(glp_prob *lp, int i)
alpar@1: {     /*struct LPXCPS *cps = lp->cps;*/
alpar@1:       double dval;
alpar@1:       if (!(1 <= i && i <= lp->m))
alpar@1:          xerror("glp_ipt_row_dual: i = %d; row number out of range\n",
alpar@1:             i);
alpar@1:       dval = lp->row[i]->dval;
alpar@1:       /*if (cps->round && fabs(dval) < 1e-9) dval = 0.0;*/
alpar@1:       return dval;
alpar@1: }
alpar@1: 
alpar@1: /***********************************************************************
alpar@1: *  NAME
alpar@1: *
alpar@1: *  glp_ipt_col_prim - retrieve column primal value (interior point)
alpar@1: *
alpar@1: *  SYNOPSIS
alpar@1: *
alpar@1: *  double glp_ipt_col_prim(glp_prob *lp, int j);
alpar@1: *
alpar@1: *  RETURNS
alpar@1: *
alpar@1: *  The routine glp_ipt_col_prim returns primal value of the structural
alpar@1: *  variable associated with j-th column. */
alpar@1: 
alpar@1: double glp_ipt_col_prim(glp_prob *lp, int j)
alpar@1: {     /*struct LPXCPS *cps = lp->cps;*/
alpar@1:       double pval;
alpar@1:       if (!(1 <= j && j <= lp->n))
alpar@1:          xerror("glp_ipt_col_prim: j = %d; column number out of range\n"
alpar@1:             , j);
alpar@1:       pval = lp->col[j]->pval;
alpar@1:       /*if (cps->round && fabs(pval) < 1e-9) pval = 0.0;*/
alpar@1:       return pval;
alpar@1: }
alpar@1: 
alpar@1: /***********************************************************************
alpar@1: *  NAME
alpar@1: *
alpar@1: *  glp_ipt_col_dual - retrieve column dual value (interior point)
alpar@1: *
alpar@1: *  SYNOPSIS
alpar@1: *
alpar@1: *  #include "glplpx.h"
alpar@1: *  double glp_ipt_col_dual(glp_prob *lp, int j);
alpar@1: *
alpar@1: *  RETURNS
alpar@1: *
alpar@1: *  The routine glp_ipt_col_dual returns dual value (i.e. reduced cost)
alpar@1: *  of the structural variable associated with j-th column. */
alpar@1: 
alpar@1: double glp_ipt_col_dual(glp_prob *lp, int j)
alpar@1: {     /*struct LPXCPS *cps = lp->cps;*/
alpar@1:       double dval;
alpar@1:       if (!(1 <= j && j <= lp->n))
alpar@1:          xerror("glp_ipt_col_dual: j = %d; column number out of range\n"
alpar@1:             , j);
alpar@1:       dval = lp->col[j]->dval;
alpar@1:       /*if (cps->round && fabs(dval) < 1e-9) dval = 0.0;*/
alpar@1:       return dval;
alpar@1: }
alpar@1: 
alpar@1: /* eof */