MATLAB: How to do Exhaustive search in matlab

Question

I have a function that depends on three variables x,y,z. I want to find the optimal values of these variables using exhaustive search that can maximize this function, subject to x+y+z<=1. How can I do this in Matlab?

Answer 1

xvalues = [list all possible x values]
yvalues = [list all possible y values]
zvalues = [list all possible z values];
[X, Y, Z] = ndgrid(xvalues, yvalues, zvalues);
mask = X + Y + Z <=1;
x = X(mask);
y = Y(mask);
z = Z(mask);
f = x.^3 - log(y+z) + sin(z);  %compute everything. %use appropriate function
[bestf, bestidx] = min(f);     %or max(f) depending what you are trying to optimize
bestx = x(bestidx);
besty = y(bestidx);
bestz = z(bestidx);