Styblinski-Tang

Problem definition

Objective function
f = @(x) (x(:,1).^4 - 16*x(:,1).^2 + 5*x(:,1) + x(:,2).^4 - 16*x(:,2).^2 + 5*x(:,2))/2
Optimization settings
o = struct	

% initializing struct

o.lb = -5

% lower bounds

o.ub = 5

% upper bounds

Graphic representation
[x,y] = meshgrid(o.lb:0.5:o.ub)
surf(x,y,f([x(:),y(:)]))

Problem properties

convexity smoothness minimum
0 f(-2.903534,-2.903534) = -78.332

Optimization example with fminsearch

Optimization
rng(0)	

% for tractability

x0 = [3,3]

% initial guess

[xmin,fmin,info] = fminsearch(f,x0,o)

% running minimization

Animation
rng(0)
x0 = [3,3]
[~,~,info] = fminsearch(f,x0,o)
info.sol = [-2.903534 -2.903534 -78.332]	

% solution

info.animate = true

% plot animation

info.animfreq = 5

% frame frequency

info.np = 20

% number of points for meshgrid

optimview('fminsearch',info)

References

[1] M.A. Styblinski and T.S. Tang, "Experiments in nonconvex optimization: Stochastic approximation with function smoothing and simulated annealing", Neural Networks 3, 467-483, 1990

Related functions

fminsearch | meshgrid | surf