The Linear Programming (LP) Solver

Procedures in Online Documentation

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



is the vector of decision variables

is the matrix of constraints

is the vector of objective function coefficients

is the vector of constraints right-hand sides (RHS)

is the vector of lower bounds on variables

is the vector of upper bounds on variables

The following LP solvers are available in the OPTMODEL procedure:

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.


LP solvers examples