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



is the vector of decision variables 



is the matrix of constraints 



is the vector of objective function coefficients 



is the vector of constraints righthand 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:
primal simplex solver
dual simplex solver
interior point solver (experimental)
The simplex solvers implement the twophase 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 primaldual predictorcorrector interior point algorithm. If any of the decision variables are constrained to be integervalued, 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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