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# Copyright (c) 1997-2024
# Ewgenij Gawrilow, Michael Joswig, and the polymake team
# Technische Universität Berlin, Germany
# https://polymake.org
#
# This program is free software; you can redistribute it and/or modify it
# under the terms of the GNU General Public License as published by the
# Free Software Foundation; either version 2, or (at your option) any
# later version: http://www.gnu.org/licenses/gpl.txt.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#-------------------------------------------------------------------------------
# @category Optimization
# A mixed integer linear program specified by a linear or abstract objective function
# @relates objects/Polytope
# @tparam Scalar numeric type of variables and objective function
declare object MixedIntegerLinearProgram<Scalar=Rational> {
# Linear objective funtion. In d-space a linear objective function is given
# by a (d+1)-vector. The first coordinate specifies a constant that is
# added to the resulting value.
# @example [require bundled:scip]
# The following defines a MixedIntegerLinearProgram together with a
# linear objective on a rational line segment embedded in two-dimensional
# space.
# > $l = new Polytope(INEQUALITIES=>[[0,1,0],[3/2,-1,0],[1,0,0]],EQUATIONS=>[[0,0,1]]);
# > $obj = new Vector([0,-1,0]);
# > $intvar = new Set<Int>([0,1,2]);
# > $milp = $l->MILP(LINEAR_OBJECTIVE=>$obj, INTEGER_VARIABLES=>$intvar);
# > print $milp->LINEAR_OBJECTIVE;
# | 0 -1 0
property LINEAR_OBJECTIVE : Vector<Scalar>;
# Similar to [[MAXIMAL_VALUE]].
# @example [require bundled:scip]
# The following defines a MixedIntegerLinearProgram together with a
# linear objective on a rational line segment embedded in two-dimensional
# space. Note that the maximal value is integral and not the same as the
# value of the objective function on any of the vertices.
# > $l = new Polytope(INEQUALITIES=>[[0,1,0],[3/2,-1,0],[1,0,0]],EQUATIONS=>[[0,0,1]]);
# > $obj = new Vector([0,-1,0]);
# > $intvar = new Set<Int>([0,1,2]);
# > $milp = $l->MILP(LINEAR_OBJECTIVE=>$obj, INTEGER_VARIABLES=>$intvar);
# > print $milp->MINIMAL_VALUE;
# | -1
# @example [require bundled:scip]
# Same as the previous example, but we do not require the first
# coordinate to be integral anymore.
# > $l = new Polytope(INEQUALITIES=>[[0,1,0],[3/2,-1,0],[1,0,0]],EQUATIONS=>[[0,0,1]]);
# > $obj = new Vector([0,-1,0]);
# > $intvar = new Set<Int>([0,2]);
# > $milp = $l->MILP(LINEAR_OBJECTIVE=>$obj, INTEGER_VARIABLES=>$intvar);
# > print $milp->MINIMAL_VALUE;
# | -3/2
property MINIMAL_VALUE : Scalar;
# Similar to [[MAXIMAL_SOLUTION]]
# @example [require bundled:scip]
# The following defines a MixedIntegerLinearProgram together with a
# linear objective for the centered square with side length 2 and asks for a
# maximal solution:
# > $c = new Vector([0, 1, -1/2]);
# > $p = cube(2);
# > $p->MILP(LINEAR_OBJECTIVE=>$c);
# > print $p->MILP->MINIMAL_SOLUTION;
# | 1 -1 1
property MINIMAL_SOLUTION : Vector<Scalar>;
# Maximum value the objective funtion takes under the restriction given by
# [[INTEGER_VARIABLES]].
# @example [require bundled:scip]
# The following defines a MixedIntegerLinearProgram together with a
# linear objective on a rational line segment embedded in two-dimensional
# space. Note that the maximal value is integral and not the same as the
# value of the objective function on any of the vertices.
# > $l = new Polytope(INEQUALITIES=>[[0,1,0],[3/2,-1,0],[1,0,0]],EQUATIONS=>[[0,0,1]]);
# > $obj = new Vector([0,1,0]);
# > $intvar = new Set<Int>([0,1,2]);
# > $milp = $l->MILP(LINEAR_OBJECTIVE=>$obj, INTEGER_VARIABLES=>$intvar);
# > print $milp->MAXIMAL_VALUE;
# | 1
# @example [require bundled:scip]
# Same as the previous example, but we do not require the first
# coordinate to be integral anymore.
# > $l = new Polytope(INEQUALITIES=>[[0,1,0],[3/2,-1,0],[1,0,0]],EQUATIONS=>[[0,0,1]]);
# > $obj = new Vector([0,1,0]);
# > $intvar = new Set<Int>([0,2]);
# > $milp = $l->MILP(LINEAR_OBJECTIVE=>$obj, INTEGER_VARIABLES=>$intvar);
# > print $milp->MAXIMAL_VALUE;
# | 3/2
property MAXIMAL_VALUE : Scalar;
# Coordinates of a (possibly not unique) affine vertex at which the maximum
# of the objective function is attained.
# @example [require bundled:scip]
# The following defines a MixedIntegerLinearProgram together with a
# linear objective for the centered square with side length 2 and asks for a
# maximal solution:
# > $c = new Vector([0, 1, -1/2]);
# > $p = cube(2);
# > $p->MILP(LINEAR_OBJECTIVE=>$c);
# > print $p->MILP->MAXIMAL_SOLUTION;
# | 1 1 -1
# @example [require bundled:scip]
# The following defines a MixedIntegerLinearProgram together with a
# linear objective on a rational line segment embedded in two-dimensional
# space. Note that the maximal solution is not a vertex/endpoint of the line
# segment.
# > $l = new Polytope(INEQUALITIES=>[[0,1,0],[3/2,-1,0],[1,0,0]],EQUATIONS=>[[0,0,1]]);
# > $obj = new Vector([0,1,0]);
# > $intvar = new Set<Int>([0,1,2]);
# > $milp = $l->MILP(LINEAR_OBJECTIVE=>$obj, INTEGER_VARIABLES=>$intvar);
# > print $milp->MAXIMAL_SOLUTION;
# | 1 1 0
# @example [require bundled:scip]
# Same as the previous example, but we do not require the first
# coordinate to be integral anymore. Now the maximal solution is an endpoint
# of the line segment.
# > $l = new Polytope(INEQUALITIES=>[[0,1,0],[3/2,-1,0],[1,0,0]],EQUATIONS=>[[0,0,1]]);
# > $obj = new Vector([0,1,0]);
# > $intvar = new Set<Int>([0,2]);
# > $milp = $l->MILP(LINEAR_OBJECTIVE=>$obj, INTEGER_VARIABLES=>$intvar);
# > print $milp->MAXIMAL_SOLUTION;
# | 1 3/2 0
property MAXIMAL_SOLUTION : Vector<Scalar>;
# Set of integers that indicate which entries of the solution should be
# integral. If no value is specified, all entries are required to be
# integral. If all entries should be rational, please use an
# [[LinearProgram]] instead.
# @example [require bundled:scip]
# The following defines a MixedIntegerLinearProgram together with a
# linear objective on a rational line segment embedded in two-dimensional
# space.
# > $l = new Polytope(INEQUALITIES=>[[0,1,0],[3/2,-1,0],[1,0,0]],EQUATIONS=>[[0,0,1]]);
# > $obj = new Vector([0,1,0]);
# > $intvar = new Set<Int>([0,1,2]);
# > $milp = $l->MILP(LINEAR_OBJECTIVE=>$obj, INTEGER_VARIABLES=>$intvar);
# > print $milp->INTEGER_VARIABLES;
# | {0 1 2}
# @example [require bundled:scip]
# Same as the previous example, but we do not require the first
# coordinate to be integral anymore.
# > $l = new Polytope(INEQUALITIES=>[[0,1,0],[3/2,-1,0],[1,0,0]],EQUATIONS=>[[0,0,1]]);
# > $obj = new Vector([0,1,0]);
# > $intvar = new Set<Int>([0,2]);
# > $milp = $l->MILP(LINEAR_OBJECTIVE=>$obj, INTEGER_VARIABLES=>$intvar);
# > print $milp->INTEGER_VARIABLES;
# | {0 2}
property INTEGER_VARIABLES : Set<Int>;
}
object Polytope {
# @category Optimization
# Mixed integer linear program applied to the polytope
property MILP : MixedIntegerLinearProgram<Scalar> : multiple;
}
# Local Variables:
# mode: perl
# cperl-indent-level: 3
# indent-tabs-mode:nil
# End:
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