Appendix A MATLAB's Optimization Toolbox Algorithms

Abstract

MATLAB's Optimization Toolbox (version 7:2) includes a family of algorithms for solving optimization problems. The toolbox provides functions for solving linear programming, mixed-integer linear programming, quadratic programming , nonlinear programming, and nonlinear least squares problems. This chapter presents the available functions of this toolbox for solving LPs. A computational study is performed. The aim of the computational study is to compare the efficiency of MATLAB's Optimization Toolbox solvers. A.1 Chapter Objectives • Present the linear programming algorithms of MATLAB's Optimization Toolbox. • Understand how to use the linear programming solver of MATLAB's Optimization Toolbox. • Present all different ways to solve linear programming problems using MAT-LAB. • Compare the computational performance of the linear programming algorithms of MATLAB's Optimization Toolbox. A.2 Introduction MATLAB is a matrix language intended primarily for numerical computing. MATLAB is especially designed for matrix computations like solving systems of linear equations or factoring matrices. Users that are not familiar with MATLAB are referred to [3, 7]. Experienced MATLAB users that want to further optimize their codes are referred to [1]. MATLAB's Optimization Toolbox includes a family of algorithms for solving optimization problems. The toolbox provides functions for solving linear programming , mixed-integer linear programming, quadratic programming, nonlinear programming, and nonlinear least squares problems. MATLAB's Optimization Toolbox includes four categories of solvers [9]: