Optimization Toolbox

Nonlinear Least-Squares, Data Fitting, and Nonlinear Equations

Optimization Toolbox can solve linear and nonlinear least-squares problems, data fitting problems, and nonlinear equations.

Linear and Nonlinear Least-Squares Optimization

The toolbox uses two algorithms for solving constrained linear least-squares problems:

• The medium-scale algorithm implements an active-set algorithm and is used to solve problems with bounds and linear inequalities or equalities. 
• The large-scale algorithm implements a trust-region reflective algorithm and is used to solve problems that have only bound constraints.

The toolbox uses two algorithms for solving nonlinear least-squares problems:

• The trust-region reflective algorithm implements the Levenberg-Marquardt algorithm using a trust-region approach. It is used for unconstrained and bound-constrained problems.
• The Levenberg-Marquardt algorithm implements a standard Levenberg-Marquardt method. It is used for unconstrained problems.

Fitting a transcendental equation using nonlinear least squares.

Data Fitting

The toolbox provides a specialized interface for data fitting problems in which you want to find the member of a family of nonlinear functions that best fits a set of data points. The toolbox uses the same algorithms for data fitting problems that it uses for nonlinear least-squares problems.

Fitting a nonlinear exponential equation using least-squares curve fitting.

Nonlinear Equation Solving

Optimization Toolbox implements a dogleg trust-region algorithm for solving a system of nonlinear equations where there are as many equations as unknowns. The toolbox can also solve this problem using the trust-region reflective and Levenberg-Marquardt algorithms.

Solving an n-dimensional Rosenbrock function using the nonlinear equation solver.