Adjiman
Problem definition
Objective function
f = @(x) cos(x(:,1)).*sin(x(:,2)) - x(:,1)./(x(:,2).^2 + 1)
Optimization settings
o = struct% initializing struct
o.lb = -1% lower bounds
o.ub = 2% upper bounds
Graphic representation
[x,y] = meshgrid(-1:0.2:2) surf(x,y,f([x(:),y(:)]))
Problem properties
convexity | smoothness | minimum |
0 | ∞ | f(2, 0.10578) = -2.02181 |
Optimization example with fminsearch
Optimization
rng(0)% for tractability
x0 = [-0.2,1.2]% initial guess
[xmin,fmin,info] = fminsearch(f,x0,o)% running minimization
Animation
rng(0) x0 = [-0.2,1.2] [~,~,info] = fminsearch(f,x0,o) info.sol = [2 0.10578 -2.02181]% solution
info.animate = true% plot animation
info.animfreq = 5% frame frequency
info.np = 16% number of points for meshgrid
optimview('fminsearch',info)
References
[1] C. S. Adjiman, S. Sallwig, C. A. Flouda, A. Neumaier, "A Global Optimization
Method, aBB for General Twice-Differentiable NLPs-1, Theoretical Advances", Computers
Chemical Engineering, vol. 22, no. 9, pp. 1137-1158, 1998