Goldstein-Price

Problem definition

Objective function
f = @(x) (1+((x(:,1) + x(:,2) + 1).^2).*(19 - 14*x(:,1) + ...
       3*x(:,1).^2 - 14*x(:,2) + 6*x(:,1).*x(:,2) + ...
       3*x(:,2).^2)).*(30 + ((2*x(:,1) - 3*x(:,2)).^2).* (18 - 32*x(:,1)+ ...
       12*x(:,1).^2 + 48*x(:,2) - 36*x(:,1).*x(:,2) + 27*x(:,2).^2))
Optimization settings
o = struct	
% initializing struct

o.d = 2	
% dimension of decision variable

o.lb = -2	
% lower bounds

o.ub = 2	
% upper bounds
Graphic representation 
[x,y] = meshgrid(o.lb:0.4:o.ub)
surf(x,y,f([x(:),y(:)]))

Problem properties

convexity smoothness minimum
0 ∞ f(0,-1) = 3

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 = [0 -1 3]	
% solution 

info.animate = true	
% plot animation 

info.animfreq = 2	
% frame frequency 

optimview('ga',info)

References

[1] A. A. Goldstein, J. F. Price, "On Descent from Local Minima", Mathematics and Computation, vol. 25, no. 115, pp. 569-574, 1971

Related functions

ga | meshgrid | surf