# fmincon step size and speed

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Hussein Ammar on 30 Oct 2019
Commented: Hussein Ammar on 3 Nov 2019
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.

Alan Weiss on 31 Oct 2019
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
Hussein Ammar on 3 Nov 2019
I think fmincon can still get good solutions for this problem. I just need to try different configurations for the parameters in optimoptions and see which one works better. Thank you.

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