Note: This page has been translated by MathWorks. Click here to see

To view all translated materials including this page, select Country from the country navigator on the bottom of this page.

To view all translated materials including this page, select Country from the country navigator on the bottom of this page.

Find minimum of unconstrained multivariable function

Nonlinear programming solver.

Finds the minimum of a problem specified by

$$\underset{x}{\mathrm{min}}f(x)$$

where *f*(*x*) is a function
that returns a scalar.

*x* is a vector or a matrix; see Matrix Arguments.

`x = fminunc(fun,x0)`

`x = fminunc(fun,x0,options)`

`x = fminunc(problem)`

```
[x,fval]
= fminunc(___)
```

```
[x,fval,exitflag,output]
= fminunc(___)
```

```
[x,fval,exitflag,output,grad,hessian]
= fminunc(___)
```

starts
at the point `x`

= fminunc(`fun`

,`x0`

)`x0`

and attempts to find a local minimum `x`

of
the function described in `fun`

. The point `x0`

can
be a scalar, vector, or matrix.

Passing Extra Parameters explains how to pass extra parameters to the objective function and nonlinear constraint functions, if necessary.

`fminunc`

is for nonlinear problems without
constraints. If your problem has constraints, generally use `fmincon`

. See Optimization Decision Table.

minimizes `x`

= fminunc(`fun`

,`x0`

,`options`

)`fun`

with
the optimization options specified in `options`

.
Use `optimoptions`

to set these
options.

finds
the minimum for `x`

= fminunc(`problem`

)`problem`

, where `problem`

is
a structure described in Input Arguments.
Create the `problem`

structure by exporting a problem
from Optimization app, as described in Exporting Your Work.

[1] Broyden, C. G. “The Convergence of a Class of Double-Rank Minimization Algorithms.” Journal Inst. Math. Applic., Vol. 6, 1970, pp. 76–90.

[2] Coleman, T. F. and Y. Li. “An Interior, Trust Region Approach for Nonlinear Minimization Subject to Bounds.” SIAM Journal on Optimization, Vol. 6, 1996, pp. 418–445.

[3] Coleman, T. F. and Y. Li. “On the Convergence of Reflective Newton Methods for Large-Scale Nonlinear Minimization Subject to Bounds.” Mathematical Programming, Vol. 67, Number 2, 1994, pp. 189–224.

[4] Davidon, W. C. “Variable Metric Method for Minimization.” A.E.C. Research and Development Report, ANL-5990, 1959.

[5] Fletcher, R. “A New Approach to Variable Metric Algorithms.” Computer Journal, Vol. 13, 1970, pp. 317–322.

[6] Fletcher, R. “Practical Methods of Optimization.” Vol. 1, Unconstrained Optimization, John Wiley and Sons, 1980.

[7] Fletcher, R. and M. J. D. Powell. “A Rapidly Convergent Descent Method for Minimization.” Computer Journal, Vol. 6, 1963, pp. 163–168.

[8] Goldfarb, D. “A Family of Variable Metric Updates Derived by Variational Means.” Mathematics of Computing, Vol. 24, 1970, pp. 23–26.

[9] Shanno, D. F. “Conditioning of Quasi-Newton Methods for Function Minimization.” Mathematics of Computing, Vol. 24, 1970, pp. 647–656.

Was this topic helpful?