Finding all existing minimums of a function

I have this function:

I need to find all existing minimums of this function using fminsearch and also draw a 3D plot with minimum points highlighted on it.

What I've tried so far:

fun2 = @(x,y)x^4+y^4-2*x^2+4*x*y-2*y^2+1
x = fminsearch(@(v) fun2(v(1),v(2)),[-5,-5])
figure
[X, Y] = meshgrid(-2:0.1:2);
surf(X,Y,fun2(X,Y));

Result doesn't seem right:

Answer 1

[Image Analyst]

If you're going to pass in matrices for x and y, like X and Y from the output of meshgrid, you're going to have to use dots in the operators in your function:

fun2 = @(x,y) x .^ 4 + y .^ 4 - 2 * x .^ 2 + 4 * x .* y - 2 * y .^2 + 1;

[Saba Asanidze]

Thank you, now plot looks good but how do I get all the minimums of my function? Right now fminsearch gives me only one point (-1.4142,1.4142) but according to Wolfram point (1.4142,-1.4142) is also a minimum.

[Image Analyst]

I don't know. If it were me, I'd do it numerically. I'd evaluate the function everywhere, like between -2 and 2 or -5 and 5 or whatever you want, and then use imregionalmin() in the Image Processing Toolbox to find the local min locations.

[Walter Roberson]

fminsearch only ever returns one location per call. If you call it with different initial values it may return a different location.