MATLAB: How to calculate the minimum of a function of two variables

Question

Hello, I am new to Matlab and encountering some difficulties Computing the minimum of a function of two variables: f(x,y)= e^(x-y) + x^2 + y^2.

Also is it possible to plot the resulting surface around the minimum?

Answer 1

One approach:

syms x y 
f(x,y) = exp(x-y) + x^2 + y^2;
Dfx = diff(f, x)
D2fx = diff(Dfx,x)
Dfy = diff(f, y)
D2fy = diff(Dfy, y)
Inflpt = solve(Dfx, Dfy, [x,y])
xs = Inflpt.x
ys = Inflpt.y
Check = [D2fx(xs,ys); D2fy(xs,ys)]
figure
fsurf(f, double([xs-2 xs+2    ys-2 ys+2]))

Since ‘Check’ is positive for both functions, ‘Inflpt’ is a minimum.

EDIT —

Added plot figure —