MATLAB: Fmincon step size and speed

fmincon

Hello all,
I'm using fmincon to solve a nonconvex optimization problem. Mainly my problem is optimizing some function over a 2D area, where the optimizing variables are the x and y coordinates of N points, so my minimizer myX for my objective function f(myX) is a (2 by N) matrix representing the x and y coordinates. For this optimization, I'm interested in changes >1 meter because my objective function is not very sensitive for small changes in x and y.
So, mainly I have these two problems:
  • The step size of fmincon is very small. I'm using this configuration for fmincon:
myoptions = optimoptions(@fmincon,'Algorithm','interior-point','Display','iter', 'FiniteDifferenceStepSize', 5,...
     'TolX', 1, 'UseParallel',1);
Example of the output:
                                            First-order      Norm of
 Iter F-count            f(x)  Feasibility   optimality         step
    0      21   -1.660633e+00    0.000e+00    7.942e-04
    1      42   -1.660634e+00    0.000e+00    7.942e-04    1.598e-03
Local minimum possible. Constraints satisfied.
fmincon stopped because the size of the current step is less than
the selected value of the step size tolerance and constraints are 
satisfied to within the default value of the constraint tolerance.
As you can see, the objective function f(myX) is slightly changing (that is also happening to x and y coordinates). In this simulation I'm starting from points that satisfy the constraints but they are very far from optimality. So, how can I change the step size of fmincon (I'm interested in steps greater than 1 meter or changes on objective function that is greater than 0.1).
  • My objective function and constraint contain integral that needs to be evaluated numerically, so fmin is very slow. Are there ways to speed up fmincon.
Best Regards and thank you in advance for your help.

Best Answer

It sounds like you need to use the Global Optimization Toolbox solver patternsearch with a large value of the MeshTolerance option, like 3/4. You should also change the InitialMeshSize option to 16 or so, and, because your objective function is slow, consider using the Cache option. You seem to have about 20 control variables, so patternsearch should work fine.
The reason I say this is that fmincon is a gradient-based solver, but your function is insensitive to small changes.
Alan Weiss
MATLAB mathematical toolbox documentation
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