Optimization Toolbox

Tools for the general optimization of linear and nonlinear functions

The Optimization Toolbox contains routines that implement the most widely used methods for performing minimization or maximization on general nonlinear functions. These routines may be used to solve complex design problems in order to improve cost, reliability, and performance in a wide range of applications.

Graphically, an optimization problem can be visualized as trying to find the lowest (or highest) point in a complex, highly contoured landscape. An optimization algorithm can thus be likened to an explorer wandering through valleys and across plains in search of the topological extremes.

Features

Unconstrained nonlinear minimization
Nonlinear least squares and nonlinear data fitting
Nonlinear equation solving
Linear programming
Quadratic programming
Constrained nonlinear minimization
Constrained linear least squares
Minimax
Multi-objective optimization
Semi-infinite minimization

Highlights

Flexible Optimization Environment. With its extensive numerical capabilities and its fully extensible environment, MATLAB is an ideal system for setting up and solving optimization problems. The interactive nature of MATLAB allows optimization problems to be easily refined and adapted, providing the user with valuable feedback and insight into a problem's "best" solution. Cost functions and constraints are easily formulated in MATLAB and then solved using the functions in the Optimization Toolbox.

Nonlinear Optimization Routines. The toolbox features a variety of nonlinear optimization routines, which are designed to work with scalars, vectors, and matrices. The function to be optimized can be written as a MATLAB function or as an expression. Default optimization parameters are used extensively, but can be changed through an optional parameter vector. Parameters can be passed directly to the functions, eliminating the need for global variables.

Gradients are calculated automatically using an adaptive finite-difference method, unless they are supplied in a function. You can check supplied gradients against those calculated via finite differences.

State-of-the-Art Algorithms. The toolbox provides the latest implementations of leading optimization algorithms:

For unconstrained minimization: Nelder-Mead simplex search method and BFGS quasi-Newton method
For constrained minimization, minimax, multi-objective, and semi-infinite optimization: variations of the sequential quadratic programming method
For nonlinear least-squares problems: Gauss-Newton and Levenberg-Marquardt methods
For linear and quadratic programming, and constrained linear least-squares problems: projection method

Stefan Steinhaus, webmaster@steinhaus-net.de