The OPTMODEL procedure provides a framework for specifying and solving linear programs (LPs). A standard linear program has the following 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
network simplex solver
interior point solver
The primal and dual 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 network simplex solver extracts a network substructure, solves this using network simplex, and then constructs an advanced basis to feed to either primal or dual simplex. 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.