What Is Optimization Toolbox?

linprogNonzero elements of the vectors in the fields of lambda indicate activeconstraints at the solution. In this case, the second and third inequalityconstraints (in lambda.ineqlin) and the first lower bound constraint(in lambda.lower) are active constraints (i.e., the solution is on theirconstraint boundaries).AlgorithmLarge-Scale OptimizationThe large-scale method is based on LIPSOL (Linear Interior PointSolver, [3]), which is a variant of Mehrotra’s predictor-correctoralgorithm ([2]), a primal-dual interior-point method. A number ofpreprocessing steps occur before the algorithm begins to iterate. See“Large-Scale Linear Programming” on page 4-15.Medium-Scale Optimizationlinprog uses a projection method as used in the quadprog algorithm.linprog is an active set method and is thus a variation of thewell-known simplex method for linear programming [1]. The algorithmfinds an initial feasible solution by first solving another linearprogramming problem.Alternatively, you can use the simplex algorithm, described in “SimplexAlgorithm” on page 3-39, by enteringoptions = optimset('LargeScale', 'off', 'Simplex', 'on')and passing options as an input argument to linprog. Thesimplexalgorithm returns a vertex optimal solution.Note You cannot supply an initial point x0 for linprog with eitherthe large-scale method or the medium-scale method using the simplexalgorithm. In either case, if you pass in x0 as an input argument,linprog ignores x0 and computes its own initial point for the algorithm.8-136