CPLEX abc2gap

This page is part of the CPLEX Manual. See CPLEX.

Purpose

Converting a general assignment problem (GAP) to a standard form suitable for a MIP solver.

The GAP problem is formulated as

${\begin{array}{cl}\min \limits _{x_{ij}}&f(x)=\sum _{i=1}^{m}\sum _{j=1}^{n}c_{ij}*x_{ij}\\&\\s/t&\sum _{j=1}^{n}x_{ij}=1~~,i=1,...,m\\&\sum _{i=1}^{m}a_{ij}*x_{ij}\leq b_{j}~~,j=1,..,n\\&x\in B^{m\times n},B=\{0,1\}.\\\end{array}}$

Calling Syntax

[c, x L, x U, b L, b U, a, sos1] = abc2gap( A, b, C, SOS1);

Description of Input

Input	Description
A	A m × n constraint matrix for GAP constraints.
b	A m × 1 right hand side vector.
C	A m × n cost matrix for GAP constraints.
SOS1	Logical variable, default false. If true, generate output for sos1 handling with CPLEX. Otherwise generate output giving an equivalent formulation with standard integer variables.

Description of Output

Output	Description
c	Linear objective function cost coefficients, vector m * n × 1.
x_L	Lower bounds on design parameters x.
x_U	Upper bounds on design parameters x.
b_ L	Lower bounds on the m + n linear constraints.
b_U	Upper bounds on the linear constraints.
a	Sparse m + n × m * n matrix for linear constraints.
sos1	If input variable SOS1 is true, structure with sos1 variable information in the form suitable for the Matlab CPLEX interface routine cplex.m, otherwise empty.

Description

Converting a general assignment problem (GAP) to standard form suitable for a mixed-integer programming solver. Either binary or sos1 variables are used.