Holder table

Problem definition

Objective function
f = @(x) -abs(sin(x(:,1)).*cos(x(:,2)).*exp(abs(1 - (sqrt(x(:,1).^2 + x(:,2).^2)./pi))))
Optimization settings
o = struct	

% initializing struct

o.d = 2

% dimension of decision variable

o.lb = -10

% lower bounds

o.ub = 10

% upper bounds

Graphic representation
[x,y] = meshgrid(-10:0.4:10)
surf(x,y,f([x(:),y(:)]))

Problem properties

convexity smoothness minimum
0 f(-8.05502, 9.66459) = -19.2085

Optimization example with ga

Optimization
rng(0)	

% for tractability

[xmin,fmin,popPos,popCost] = ga(f,o)

% running minimization

Animation
rng(0)
[~,~,~,~,info] = ga(f,o)
info.sol = [-8.05502 9.66459 -19.2085]	

% solution

info.animate = true

% plot animation

info.animfreq = 2

% frame frequency

info.np = 40

% number of points for meshgrid

optimview('ga',info)

References

[1] S. K. Mishra, "Global Optimization By Differential Evolution and Particle Swarm Methods: Evaluation On Some Benchmark Functions", Munich Research Papers in Economics

Related functions

ga | meshgrid | surf