Local minimum and global minimum of a function

Hi!

I need to obtain the first local minimum as well as the global minimum of this function for t>0.

CV_inf = @(T) T.*(4/(n+1)) - (1/2*pi)*integral(psitildasq,(-T),(T),'Arrayvalued',true);

where

psitildasq = @(t) (1/n^2)*sum((cos(x.*t))).^2 + (1/n^2)*sum((sin(x.*t))).^2;

n is the size of vector x.

Beacause fmnbnd and fminsearch may give local minimum of a function, are there other functions that I can use? If so is there an option I could specify to obtain the first local minimum?

Thanks.

[Walter Roberson]

Consider moving the n out of psitildasq to speed the integration up. It is acting as a constant multiplier of 1/n^2 on the integral.

Question: do you intend 1/2*pi to be pi/2 or to be 1/(2*pi) ?

Answer 1

[Walter Roberson]

patternsearch() from the Global Optimization Toolbox might be appropriate for the global minimum.