The Linear Programming Solver

The linear programming (LP) solver in the OPTMODEL procedure enables you to solve linear programming problems. A standard linear program has the formulation

$\text{[math]}$

where

$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	is the vector of decision variables
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	is the matrix of constraints
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	is the vector of objective function coefficients
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	is the vector of constraints right-hand sides (RHS)
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	is the vector of lower bounds on variables
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	is the vector of upper bounds on variables

The following LP solvers are available in the OPTMODEL 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. If any of the decision variables are constrained to be integer-valued, then the relaxed version of the problem is solved.

For further details, see the SAS/OR^® User's Guide: Mathematical Programming: The Linear Programming Solver.
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The Linear Programming Solver

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