|MATLAB Function Reference|
Minimize a function of several variables
x = fmins('fun',x0)
returns a vector
x which is a local minimizer of
fun(x) near .
x = fmins('fun',x0,options)
does the same as the above, but uses
options control parameters.
x = fmins('fun',x0,options,,P1,P2,...)
does the same as above, but passes arguments to the objective function,
...). Pass an empty matrix for
options to use the default value.
[x,options] = fmins(...)
options(10), a count of the number of steps taken.
||Arguments to be passed to fun.
||Argument needed to provide compatibility with
||A string containing the name of the objective function to be minimized.
||A vector of control parameters. Only four of the 18 components of
A classic test example for multidimensional minimization is the Rosenbrock banana function
The minimum is at
(1,1) and has the value
0. The traditional starting point is
(-1.2,1). The M-file
banana.m defines the function.
This indicates that the minimizer was found to at least four decimal places in 165 steps.
Move the location of the minimum to the point
[a,a^2] by adding a second parameter to
Then the statement
sets the new parameter to
sqrt(2) and seeks the minimum to an accuracy higher than the default.
The algorithm is the Nelder-Mead simplex search described in the two references. It is a direct search method that does not require gradients or other derivative information. If
n is the length of
x, a simplex in
n-dimensional space is characterized by the
n+1 distinct vectors which are its vertices. In two-space, a simplex is a triangle; in three-space, it is a pyramid.
At each step of the search, a new point in or near the current simplex is generated. The function value at the new point is compared with the function's values at the vertices of the simplex and, usually, one of the vertices is replaced by the new point, giving a new simplex. This step is repeated until the diameter of the simplex is less than the specified tolerance.
foptions in the Optimization Toolbox (or type
 Nelder, J. A. and R. Mead, "A Simplex Method for Function Minimization," Computer Journal, Vol. 7, p. 308-313.
 Dennis, J. E. Jr. and D. J. Woods, "New Computing Environments: Microcomputers in Large-Scale Computing," edited by A. Wouk, SIAM, 1987, pp. 116-122.