Booth
Problem definition
Objective function
f = @(x) (x(:,1) + 2*x(:,2) - 7).^2 + (2*x(:,1) + x(:,2) - 5).^2
Optimization settings
o = struct% initializing struct
o.lb = -10% lower bounds
o.ub = 10% upper bounds
Graphic representation
[x,y] = meshgrid(o.lb:2:o.ub) surf(x,y,f([x(:),y(:)]))
Problem properties
convexity | smoothness | minimum |
1 | ∞ | f(1,3) = 0 |
Optimization example with fminsearch
Optimization
rng(0)% for tractability
x0 = [5,-5]% initial guess
[xmin,fmin,info] = fminsearch(f,x0,o)% running minimization
Animation
rng(0) x0 = [5,-5] [~,~,info] = fminsearch(f,x0,o) info.sol = [1 3 0]% solution
info.animate = true% plot animation
info.animfreq = 5% frame frequency
optimview('fminsearch',info)