Optimization Toolbox 4.1

Product Description

• Introduction and Key Features
• Defining, Solving, and Assessing Optimization Problems
• Nonlinear Optimization and Multi-Objective Optimization
• Nonlinear Least-Squares, Data Fitting, and Nonlinear Equations
• Quadratic, Linear, and Binary Integer Programming
• Solving Optimization Problems Using Parallel Computing

Nonlinear Least-Squares, Data Fitting, and Nonlinear Equations

Optimization Toolbox can solve nonlinear least squares problems, data fitting problems, and systems of nonlinear equations.

The toolbox uses three methods for solving nonlinear least squares problems: trust-region, Levenberg-Marquardt, and Gauss-Newton.

Levenberg-Marquardt is a method whose search direction is a cross between the Gauss-Newton and steepest descent directions.

Trust-region implements the Levenberg-Marquardt algorithm using trust regions. It is used for unconstrained and bound constrained problems.

Gauss-Newton is a line search method that chooses a search direction based on the solution to a linear least-squares problem.

The toolbox also includes a specialized interface for data-fitting problems to find the member of a family of nonlinear functions that best fits a set of data points. The toolbox uses the same methods for data-fitting problems as it uses for nonlinear least-squares problems.

Optimization Toolbox implements a dogleg trust region method for solving a system of nonlinear equations where there are as many equations as unknowns. The toolbox can also solve this problem using either the trust-region, the Levenberg-Marquandt, or the Gauss-Newton method.