The OPTLP Procedure

Overview: OPTLP Procedure

The OPTLP procedure provides three methods of solving linear programs (LPs). A linear program has the following formulation:

$\displaystyle\mathop{\min} & \mathbf{c}^{\rm t} \mathbf{x} \ {subject to} & \m... ...x}\;\{\ge, =, \le\}\; \mathbf{b} \ & \mathbf{l} \le \mathbf{x} \le \mathbf{u}$

where

$\mathbf{x}$	$\in$	$\mathbb{r}^n$	is the vector of decision variables
$\mathbf{a}$	$\in$	$\mathbb{r}^{m x n}$	is the matrix of constraints
$\mathbf{c}$	$\in$	$\mathbb{r}^n$	is the vector of objective function coefficients
$\mathbf{b}$	$\in$	$\mathbb{r}^m$	is the vector of constraints right-hand sides (RHS)
$\mathbf{l}$	$\in$	$\mathbb{r}^n$	is the vector of lower bounds on variables
$\mathbf{u}$	$\in$	$\mathbb{r}^n$	is the vector of upper bounds on variables

The following LP solvers are available in the OPTLP procedure:

primal simplex solver
dual simplex solver
interior point solver (experimental)

The simplex solvers implement the two-phase simplex method. In phase I, the solver tries to find a feasible solution. If no feasible solution is found, the LP is infeasible; otherwise, the solver enters phase II to solve the original LP. The interior point solver implements a primal-dual predictor-corrector interior point algorithm.

PROC OPTLP requires a linear program to be specified using a SAS data set that adheres to the MPS format, a widely accepted format in the optimization community. For details about the MPS format see Chapter 14, "The MPS-Format SAS Data Set."

You can use the MPSOUT= option to convert typical PROC LP format data sets into MPS-format SAS data sets. The option is available in the LP, INTPOINT, and NETFLOW procedures. For details about this option, see Chapter 3, "The LP Procedure," Chapter 2, "The INTPOINT Procedure," and Chapter 5, "The NETFLOW Procedure."

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