Easom
Problem definition
Objective function
f = @(x) -cos(x(:,1)).*cos(x(:,2)).*exp(-((x(:,1)-pi).^2 + (x(:,2)-pi).^2))
Optimization settings
o = struct% initializing struct
o.lb = 1% lower bounds
o.ub = 5% upper bounds
Graphic representation
[x,y] = meshgrid(1:0.2:5) surf(x,y,f([x(:),y(:)]))
Problem properties
convexity | smoothness | minimum |
1 | ∞ | f(pi,pi)=-1 |
Optimization example with fminsearch
Optimization
rng(0)% for tractability
x0 = [2.1,3]% initial guess
[xmin,fmin,info] = fminsearch(f,x0,o)% running minimization
Animation
rng(0) x0 = [2.1,3] [~,~,info] = fminsearch(f,x0,o) info.sol = [pi pi -1]% solution
info.animate = true% plot animation
info.animfreq = 6% frame frequency
info.np = 20% number of points for meshgrid
optimview('fminsearch',info)