Elias: Created page with "{{Part Of Manual|title=the CPLEX Manual|link=CPLEX}} ==Purpose== Converting a general assignment problem (GAP) to a standard form suitable for a MIP solver. The GAP p..."

2011-08-15T15:17:05Z

Created page with "{{Part Of Manual|title=the CPLEX Manual|link=CPLEX}} ==Purpose== Converting a general assignment problem (GAP) to a standard form suitable for a MIP solver. The GAP p..."

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{{Part Of Manual|title=the CPLEX Manual|link=[[CPLEX|CPLEX]]}}
==Purpose==

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

The GAP problem is formulated as

<math>
\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}
</math>

==Calling Syntax==

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

==Description of Input==

{| class="wikitable"
!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==

{| class="wikitable"
!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 ''SOS''1 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.

CPLEX abc2gap - Revision history

Elias: Created page with "{{Part Of Manual|title=the CPLEX Manual|link=CPLEX}} ==Purpose== Converting a general assignment problem (GAP) to a standard form suitable for a MIP solver. The GAP p..."