Optimization Toolbox

Examples that Use Standard Algorithms

This section presents the medium-scale (i.e., standard) algorithms through a tutorial. Examples similar to those in the first part of this tutorial (Unconstrained Minimization Example through the Equality Constrained Example) can also be found in the first demonstration, "Tutorial Walk Through," in the M-file optdemo. The examples in this manual differ in that they use M-file functions for the objective functions, whereas the online demonstrations use inline objects for some functions.

Note    Medium-scale is not a standard term and is used to differentiate these algorithms from the large-scale algorithms described in Large-Scale Algorithms.

The tutorial uses the functions fminunc, fmincon, and fsolve. The other optimization routines, fgoalattain, fminimax, lsqnonlin, and fseminf, are used in a nearly identical manner, with differences only in the problem formulation and the termination criteria. The section Multiobjective Examples discusses multiobjective optimization and gives several examples using lsqnonlin, fminimax, and fgoalattain, including how Simulink can be used in conjunction with the toolbox.

This section includes the following examples:

• Unconstrained Minimization Example
• Nonlinear Inequality Constrained Example
• Constrained Example with Bounds
• Constrained Example with Gradients
• Gradient Check: Analytic Versus Numeric
• Equality Constrained Example

It also discusses

• Maximization
• Greater-Than-Zero Constraints
• Additional Arguments: Avoiding Global Variables
• Nonlinear Equations with Analytic Jacobian
• Nonlinear Equations with Finite-Difference Jacobian
• Multiobjective Examples

Using the Optimization Functions

Unconstrained Minimization Example