# sdo.optimize

Solve design optimization problem

## Syntax

## Description

Solve an optimization problem to find the values of design variables that satisfy the design requirements.

Use `sdo.optimize`

to solve a design optimization problem of the
following form:

$$\underset{p}{\text{min}}F(p)\text{subjectto}\{\begin{array}{l}{C}_{leq}(p)\le 0\hfill \\ {C}_{eq}(p)=0\hfill \\ A\times p\le B\hfill \\ {A}_{eq}\times p={B}_{eq}\hfill \\ lb\le p\le ub\hfill \end{array}$$

Here:

*F*is the cost (objective).*p*is a scalar or vector of design variables.*C*and_{leq}*C*are the nonlinear inequality and equality constraints, respectively._{eq}*A*and*B*are the linear inequality constraints.*A*and_{eq}*B*are the linear equality constraints._{eq}*lb*and*ub*are the lower and upper bounds on*p*, respectively.

`sdo.optimize`

can optimize continuously varying parameters and
discrete-valued parameters (mixed-integer optimization). Tuning discrete-valued parameters
requires Global Optimization Toolbox software.

`[`

uses `optimParam`

,`optimInfo`

] = sdo.optimize(`optimFcn`

,`param`

)`fmincon`

, the default optimization method, to find
the parameter values `optimParam`

that satisfy the requirements specified
in `optimFcn`

.

`[`

solves the optimization problem with the optimization options specified in
`optimParam`

,`optimInfo`

] = sdo.optimize(`optimFcn`

,`param`

,`options`

)`options`

. Use `sdo.OptimizeOptions`

to set these
options.

`[`

solves the optimization problem specified in a structure `optimParam`

,`optimInfo`

] = sdo.optimize(`prob`

)`prob`

that
contains the function to be minimized, design variables, and optimization options.

## Examples

## Input Arguments

## Output Arguments

## Tips

By default, the software displays the optimization information for each iteration in the MATLAB command window. To learn more about the information displayed, see:

Iterative Display when the optimization method is specified as

`'fmincon'`

(default),`'fminsearch'`

, or`'lsqnonlin'`

Display to Command Window Options (Global Optimization Toolbox) when the optimization method is specified as

`'patternsearch'`

You can configure the level of this display using the
`MethodOptions.Display`

property of an optimization option set.

## Alternative Functionality

### Apps

The Response Optimizer app provides a graphical interface to specify design requirements and optimize model parameters. For more information, see Design Optimization to Meet a Custom Objective (GUI) and Design Optimization to Track Reference Signal (GUI).

The Parameter Estimator app provides a graphical interface to specify experiments and tune model parameters so that the model output matches the experiment data. For more information, see Estimate Model Parameter Values (GUI).

## Extended Capabilities

## Version History

**Introduced in R2011a**