Freudenstein Roth

Problem definition

Objective function
f = @(x) (x(:,1) - 13 + ((5 - x(:,2)).*x(:,2) - 2).*x(:,2)).^2 + ...
   (x(:,1) - 29 + (( x(:,2) + 1).*x(:,2) - 14).*x(:,2)).^2
Optimization settings
o = struct	
% initializing struct

o.lb = -10	
% lower bounds

o.ub = 12	
% upper bounds
Graphic representation 
[x,y] = meshgrid(o.lb:0.8:o.ub)
surf(x,y,f([x(:),y(:)]))

Problem properties

convexity smoothness minimum
1 ∞ f(11.41,-0.8968) = 48.9842

Optimization example with fminsearch

Optimization 
rng(0)	
% for tractability 

x0 = [0.5,-2]	
% initial guess 

[xmin,fmin,info] = fminsearch(f,x0,o)	
% running minimization
Animation 
rng(0)
x0 = [0.5,-2]
[~,~,info] = fminsearch(f,x0,o)
info.sol = [11.41 -0.8968 48.9842]	
% solution 

info.animate = true	
% plot animation 

info.animfreq = 5	
% frame frequency 

optimview('fminsearch',info)

References

[1] F. Freudenstein, B. Roth, "Numerical solutions of systems of nonlinear equations", 1963

Related functions

fminsearch | meshgrid | surf