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

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Daniela Würmseer on 5 Jun 2022
Commented: Walter Roberson on 6 Jun 2022
Is there (in the meantime) a better way than:
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]".
Walter Roberson on 6 Jun 2022
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.

Matt J on 6 Jun 2022
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
If you see that multiple solutions have the same objective value, it would indicate the solution is not unique.
Walter Roberson on 6 Jun 2022
... after doing uniquetol by rows to filter points that are essentially the same.

Walter Roberson on 5 Jun 2022
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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Walter Roberson on 5 Jun 2022
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.

Matt J on 6 Jun 2022
You could impose a constraint like as a smooth approximation to .
end

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