find the absolute maximum and minimum values of f on the set D

f(x,y)=exp.^(-x^2-y^2)(x^2+2y^2) with D is the disk x^2 + y^2 <=4

Answer 1

[Ameer Hamza]

Although you can use fmincon() and specify the nonlinear constraint, this function is multi-modal, and the search region is quite small, so it might be better to use a mesh and search for the smallest and largest value

f = @(x,y) exp(-x.^2-y.^2).*(x.^2+2*y.^2);
[X, Y] = meshgrid(-2:0.01:2);
mask = X.^2 + Y.^2 - 4 <= 0;
X(~mask) = nan;
Y(~mask) = nan;
Z = f(X, Y);

min_val = min(Z, [], 'all');
max_val = max(Z, [], 'all');