How can I do Exhaustive search in matlab?

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

[Walter Roberson]

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);

[Mahmoud Hasabelnaby]

If I have

for P = 1:1:10;

mask = X + Y + Z <=P; %instead of 1 only

and I want to plot (bestf,P). How can I do this?

[Walter Roberson]

Pvals = 1:10;
numP = length(Pvals);
maxP = max(Pvals);

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 <= maxP;
x = X(mask);
y = Y(mask);
z = Z(mask);
f = x.^3 - log(y+z) + sin(z);  %compute everything. %use appropriate function

bestf = zeros(1, numP);
for Pidx = 1 : numP
    P = Pvals(Pidx);
    mask = x + y + z <= P;
    bestf(Pidx) = min(f(mask));
end

plot(Pvals, bestf)

[QUANG LE]

Hello Walter, if I have two more contraints, for example: x <= y and y <= z. How can I add them to your code?

[Walter Roberson]

mask = X + Y + Z <= maxP & X <= Y & Y <= Z;

[QUANG LE]

Thanks so much, it works.