Three-Hump Camel

Problem definition

Objective function
f = @(x) 2*x(:,1).^2  - 1.05*x(:,1).^4 + x(:,1).^6/6 + x(:,1).*x(:,2) + 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
1 f(0,0) = 0

Optimization example with fminsearch

Optimization
rng(0)	

% for tractability

x0 = [4.9,2]

% initial guess

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

% running minimization

Animation
rng(0)
x0 = [4.9,2]
[~,~,info] = fminsearch(f,x0,o)
info.sol = [0 0 0]	

% solution

info.animate = true

% plot animation

info.animfreq = 5

% frame frequency

optimview('fminsearch',info)

References

[1] F. H. Branin Jr., "Widely Convergent Method of Finding Multiple Solutions of Simultaneous Nonlinear Equations", IBM Journal of Research and Development, vol. 16, no. 5, pp. 504-522, 1972

Related functions

fminsearch | meshgrid | surf