What Is Optimization Toolbox?

Constrained OptimizationSimplex AlgorithmThe simplex algorithm, invented by George Dantzig in 1947, is one of theearliest and best known optimization algorithms. The algorithm solves thelinear programming problemThe algorithm moves along the edges of the polyhedron defined by theconstraints, from one vertex to another, while decreasing the value of theobjective function, f T x, at each step. This section describes an improvedversion of the original simplex algorithm that returns a vertex optimalsolution.This section covers the following topics:• “MainAlgorithm”onpage3-39• “Preprocessing” on page 3-41• “Using the Simplex Algorithm” on page 3-41• “Basic and Nonbasic Variables” on page 3-42• “References” on page 3-42Main AlgorithmThe simplex algorithm has two phases:• Phase 1 — Compute an initial basic feasible point.• Phase 2 — Compute the optimal solution to the original problem.Note You cannot supply an initial point x0 for linprog with the simplexalgorithm. If you pass in x0 as an input argument, linprog ignores x0 andcomputes its own initial point for the algorithm.3-39