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

Related functions

fminsearch | meshgrid | surf