What Is Optimization Toolbox?

Constrained Optimization3 Updates the current solution and the current objective value.The algorithm chooses the entering and the leaving variables by solving twolinear systems while maintaining the feasibility of the solution.PreprocessingThe simplex algorithm uses the same preprocessing steps as the large-scalelinear programming solver, which are described in “Preprocessing” on page4-18. In addition, the algorithm uses two other steps:1 Eliminates columns that have only one nonzero element and eliminatestheir corresponding rows.2 For each constraint equation ,wherea is a row of Aeq, thealgorithm computes the lower and upper bounds of the linear combinationas rlb and rub if the lower and upper bounds are finite. If either rlb orrub equals b, the constraint is called a forcing constraint. Thealgorithmsets each variable corresponding to a nonzero coefficient of equal itsupper or lower bound, depending on the forcing constraint. The algorithmthen deletes the columns corresponding to these variables and deletes therows corresponding to the forcing constraints.Using the Simplex AlgorithmTo use the simplex method, set 'LargeScale' to 'off' and 'Simplex' to'on' in options.options = optimset('LargeScale', 'off', 'Simplex', 'on')Then call the function linprog with the options input argument. See thereference page for linprog for more information.linprog returns empty output arguments for x and fval if it detectsinfeasibility or unboundedness in the preprocessing procedure. linprogreturns the current point when it• Exceeds the maximum number of iterations• Detects that the problem is infeasible or unbounded in phases 1 or 23-41