# fmin

## Purpose

Minimize a function of one variable.

## Synopsis

    x = fmin('function',x1,x2)
    x = fmin('function',x1,x2,options)
    x = fmin('function',x1,x2,options,p1,p2, ...)
    [x,options] = fmin(...)

## Description

`x = fmin('function',x1,x2)` returns a value of `x` which is a local minimizer of `function(x)` in the interval `x1 < x < x2`. `function` is a string containing the name of the objective function to be minimized.

`x = fmin('function',x1,x2,options)` uses a vector of control parameters.

- If `options(1)` is nonzero, intermediate steps in the solution are displayed. The default value of `options(1)` is `0`.
- `options(2)` is the termination tolerance. The default value is 1.e-4.
- `options(14)` is the maximum number of steps. The default value is `500`.
  Only three of the 18 components of `options` are referenced by `fmin`. Other functions in the Optimization Toolbox reference the other options.

  `x = fmin('function',x1,x2,options,p1,p2,...)` provides up to 10 additional arguments which are passed to the objective function, `function(x,p1,p2,...)`.

  `[x,options] = fmin(...)` returns a count of the number of steps taken in `options(10)`.

  ## Examples

  `fmin('cos',3,4)` computes pi to a few decimal places.

  `fmin('cos',3,4,[1,1.e-12])` displays the steps taken to compute pi to 12 decimal places.

  To find the minimum of the function

  on the interval (0`,`2), write an M-file called `f.m`.

      function y = f(x)
      y = x.^3-2*x-5;

  Then invoke `fmin` with

      x = fmin('f', 0, 2)

  The result is

      x =
          0.8165

  The value of the function at the minimum is

      y = f(x)

      y =
          -6.0887

  ## Algorithm

  The algorithm is based on golden section search and parabolic interpolation. A FORTRAN program implementing the same algorithms is given in [1].

  ## See Also

      fmins, fzero
      foptions in the Optimization Toolbox

  ## References

  [1] G. E. Forsythe, M. A. Malcolm, and C. B. Moler, Computer Methods for Mathematical Computations, Prentice-Hall, 1976.

  (c) Copyright 1994 by The MathWorks, Inc.