Mathematics

Minimizing Functions of One Variable

Given a mathematical function of a single variable coded in an M-file, you can use the fminbnd function to find a local minimizer of the function in a given interval. For example, to find a minimum of the humps function in the range (0.3, 1), use

x = fminbnd(@humps,0.3,1)

which returns

x =
    0.6370

You can ask for a tabular display of output by passing a fourth argument created by the optimset command to fminbnd

x = fminbnd(@humps,0.3,1,optimset('Display','iter'))

which gives the output

Func-count      x           f(x)         Procedure
    1       0.567376      12.9098        initial
    2       0.732624      13.7746        golden
    3       0.465248      25.1714        golden
    4       0.644416      11.2693        parabolic
    5         0.6413      11.2583        parabolic
    6       0.637618      11.2529        parabolic
    7       0.636985      11.2528        parabolic
    8       0.637019      11.2528        parabolic
    9       0.637052      11.2528        parabolic

x =
     0.6370

This shows the current value of x and the function value at f(x) each time a function evaluation occurs. For fminbnd, one function evaluation corresponds to one iteration of the algorithm. The last column shows what procedure is being used at each iteration, either a golden section search or a parabolic interpolation.

Minimizing Functions and Finding Zeros

Minimizing Functions of Several Variables