How to implement fmincon() in Java for a multivariable optimization with nonlinear constraints and upper / lower boundaries?

I am translating some MATLAB code using fmicon(...) function into Java. I have been working with Cobyla, but I am not able to get the result to converge to the same solution (or even close) obtained in MATLAB.

IN MATLAB:

The call to fmincon has the form:

options=optimset('Algorithm','interior-point','Display','off');
X=fmincon(@objective,Q_old,[],[],[],[],lowerlim,upperlim,@constraint,options);

Where:

- objective(X) is a function taking X (a vector with 24 samples)

- constraint(X) is a non-linear constraint function

function [c, ceq]=constraint(X)
        [ ... function of X : g(X) ..]
        %g(X) < 1
        c=g(V)-0.99;
        ceq = [];
end

- lowerlim and upperlim are lb (lower bound) and ub (upper bound)

JAVA TRANSLATION:

I am using a Java implementation of the Cobyla library ("jcobyla"), trying to converge to the same X result as Matlab's optimization does.

It is simple to set Cobyla to obtain a good X result when no boundaries or constrains are applied. However, I am not able to successfully apply the constraint function nor the boundaries (though I defined both in the code, behaving as their equivalent in MATLAB). The Java cobyla solver stops optimizing at a certain X_suboptimal value, no matter how many times we iterate from there. I am not supplying any non-default parameters to Matlab's fmincon solver.

More information regarding my Cobyla code:

The Java "jcobyla" library implementing Cobyla can perform the min optimization, with the function:

CobylaExitStatus result = Cobyla.findMinimum(calcfc, NUM_VARIABLES, NUM_CONSTRAINTS, X0, _RHO_BEG, _RHO_END, iprint, MAX_NUM_FUNC_ITERATIONS);

Where

- calcfc is used to define the objective function (objective(X)) and the constraint function (constraint(X))

- The Cobyla internal parameter RHO controls the size of the simplex -- the value of RHO is reduced automatically from RHOBEG to RHOEND during execution. ( RHOEND, then, appears to be the same as the XTolerance parameter for the Matlab solver, where the default value = 1 e-10 ).

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My questions are:

1.Is there a better Java library/method to mimic Matlab's fmincon solver when performing a multivariable optimization with non linear constraints and upper / lower boundaries? I am not particularly committed to jcobyla, so if there's a better option, I'm open to suggestions.

2. If Cobyla is the best option, how can it be configured in a proper manner? It appears that Matlab, when running fmincon, determines the step size in a way that's not transparent to the user. Cobyla simply steps from RHO_BEG to RHO_END, but Matlab appears to recalculate the step size as it goes, which may be causing Cobyla's failure to get the same answer that fmincon does.

[Sorin C]

For example if you have boundary conditions such as 1<=x0<=2 and 0<=x1<=4 how can you represent that in Cobyla in the con double[] array? I could not get that yet...

Answer 1

[Sean de Wolski]

Why not use Compiler SDK to build a Java Class directly and avoid rewriting anything?

https://www.mathworks.com/products/matlab-compiler-sdk.html

Answer 2

[Walter Roberson]

See FiniteDifferenceStepSize in http://www.mathworks.com/help/optim/ug/fmincon.html#inputarg_options for a description of how the step size is determined. The default value appears to be sqrt(eps)

Note: you need R2016a or later to set that option. I notice you are using legacy names so you might perhaps be working with an earlier version.

[Caterina Lazaro]

Thank for the fast response Walter Roberson! We were also targeting the FiniteDifferenceStepSize of MATLAB to try generating the same step size

delta = v.*sign′(x).*max(abs(x),TypicalX);

• where sign′(x) = sign(x) except sign′(0) = 1.
• v = sqrt(eps)

However, JCobyla does not provide a direct way of including the step size into its calculations. That's why we tried to get some guidance on how configuring JCobyla or even using a different solution in Java to implement fmincon.

Thank you, Caterina Lazaro

[Walter Roberson]

I know little about Java or available Java libraries. I was responding to your remark,

"It appears that Matlab, when running fmincon, determines the step size in a way that's not transparent to the user."

by pointing to the documentation about how the step size is determined.