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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.

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