How to do "not equal to" constraints in fmincon/Global search?

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Daniela Würmseer
评论： Walter Roberson 2022-6-6
Is there (in the meantime) a better way than:
https://de.mathworks.com/matlabcentral/answers/409510-set-not-equal-to-constraint-for-a-linear-system-of-equations-solver
existing to "add" a not equal constraint to the optimization Problem?
I want to say for example "x not equal to [0,1,0,1]".
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Walter Roberson
Walter Roberson 2022-6-6
If you implemented an anti-equality constraint, fmincon would happily return the next adjacent representable number(s).
GlobalSearch is often configured to use random starting points; a trivial change in starting point is likely to return locations that are not bit-for-bit identical.
Walter Roberson
Walter Roberson 2022-6-6
Matt's suggestion of requiring a minimum distance from the distinguished point might be useful for this situation.
And possibly paretosearch() instead of global search.

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Matt J
Matt J 2022-6-6
I need to test somehow if the solution i get from Global Search is unique.
The run() command, with 5 output arguments, can return all candidate solutions located by the search
[x,fval,exitflag,output,solutions] = run(___)
If you see that multiple solutions have the same objective value, it would indicate the solution is not unique.

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Walter Roberson
Walter Roberson 2022-6-5
You could try a nonlinear equality constraint
ceq = double(isequal(x, [0 1 0 1]));
This would return 1 if the equality holds, but non-zero is disfavored. Favoured is 0 which corresponds to false which would be the case when the x is anything else.
I am not convinced that this will work well.
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John D'Errico
John D'Errico 2022-6-5
Ugh, no. This form of constraint would be discontinuous, and fmincon presumes not only continuity, but differentiability. And since fmincon will be passing in real values for the parameters, NOT integer values, exact equality will essentially never happen anyway. So I would doubt that constraint will be of any value at all.
Walter Roberson
Walter Roberson 2022-6-5
I was thinking about the continuity / differentiability when I posted that. I was thinking that it would seem plausible that you could use the nonlinear constraints to exclude (for example) a circle from consideration, and a point is a circle shrunk down to no radius. The nonlinear constraints have never been documented as being required to establish a concave area of solution.

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Matt J
Matt J 2022-6-6
You could impose a constraint like as a smooth approximation to .
function [c,ceq,gradc,gradceq]=nonlcon(x,r)
ceq=[]; gradceq=[];
gradc=[0;1;0;1]-x(:);
c=(r^2-norm(gradc)^2)/2;
end

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