Rosenbrock
Problem definition
Objective function
f = @(x) 100*(x(:,2) - x(:,1).^2).^2 + (x(:,1) - 1).^2
Graphic representation
[x,y] = meshgrid(-2:0.5:2, -1:0.5:2.5) surf(x,y,f([x(:),y(:)]))
Problem properties
| convexity | smoothness | minimum |
| 0 | ∞ | f(1,1) = 0 |
Optimization example with fminsearch
Optimization
rng(0)% for tractability
x0 = [-1.2,1]% initial guess
[xmin,fmin,info] = fminsearch(f,x0)% running minimization
Animation
rng(0) x0 = [-1.2,1] [~,~,info] = fminsearch(f,x0) info.sol = [1 1 0]% solution
info.animate = true% plot animation
info.animfreq = 5% frame frequency
optimview('fminsearch',info)
References
[1] H. H. Rosenbrock, "An Automatic Method for Finding the Greatest or Least Value of a Function", 1960