Estimate the minimum point given any function

Dear all, would like to get your help on this question!

Given any function input as a m-file,

(For example

function y = f(x)

% This is an continuous function defined on [1,2]

% where you are required to find the minimum.

y= cos(x)^2;

end )

How would you estimate the minimum point such that the estimate is within the error tolerance of 0.01?

I was thinking along this.. I can calculate the real exact value of the minimum point, but I need to use a method to estimate the minimum point so that the error between the real and the estimate is less than 0.01. But not sure what method I need to use to estimate the minimum point.

So far, Ive learnt bisection method, newton mtd, secant method in school.

THANK YOU

Answer 1

[A Jenkins]

FMINBND Single-variable bounded nonlinear function minimization.

X = FMINBND(FUN,x1,x2) attempts to find a local minimizer X of the function FUN in the interval x1 < X < x2. FUN is a function handle. FUN accepts scalar input X and returns a scalar function value F evaluated at X.

http://www.mathworks.com/help/optim/ug/fminbnd.html

Unless your professor wants you to write your own...

Answer 2

[Matt J]

You could just sample the function and use MIN, as proposed here,

http://www.mathworks.com/matlabcentral/answers/89712#answer_99158