Next: Linear Programming
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.
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.