Gramacy-Lee
Problem definition
Objective function
f = @(x) sin(10*pi*x)./(2*x) + (x-1).^4
Optimization settings
o = struct% initializing struct
o.d = 1% dimension of decision variable
o.lb = 0.5% lower bounds
o.ub = 2.5% upper bounds
Graphic representation
x = o.lb:0.01:o.ub plot(x, f(x))
Problem properties
| convexity | smoothness | minimum |
| 0 | ∞ | f(0.5485634) = -0.8690 |
Optimization example with ga
Algorithm options
o.maxit = 10% number of iterations
Optimization
rng(0)% for tractability
[xmin,fmin,popPos,popCost] = ga(f,o)% running minimization
Animation
rng(0) [~,~,~,~,info] = ga(f,o) info.sol = [0.5485634 -0.8690]% solution
info.animate = true% plot animation
info.np = 300% number of points for meshgrid
optimview('ga',info)
References
[1] R. B. Gramacy, and H. K. Lee, "Cases for the nugget in modeling computer experiments", Statistics and Computing, 22(3), 713-722, 2012