Can one solve optimization problem(in Matlab) with conditional constraint that depends on the decision variables?

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Richárd Tóth 2019-8-8

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评论： Richárd Tóth 2019-8-9

Hello

My original problem is: Find maximal volume ellipsoid(or ellipse if

), it's size is limited by

constraints, n can be higher than 3

min

s.t

and

for

where m is the number of nonlinear inequality constraints

My idea is to create a function that checks if the equation(which is the ellipsoid) has any solution with the inequality system, that is, intersects the subspace described by the inequalities. The function returns 0 if no intersection, and 1 if they intersect each other.

Then my problem would become this:

min

s.t

So the real question is: can you solve a problem like this in Matlab? You would set the intersects variable(with the mentioned function) to 0 or 1 for each

the solver tries, and accept it if the variable is 0 for the current

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Bruno Luong 2019-8-9

The loop iterates on plane constraints.

Well no that the whole advantage of such technique, I only need to check those which verifie the KT condition and there is only one of them per plane. As I told you the KT condition allows to reduce infinite number of points to finite (here is 1 per plane). No longer need to generate a bunch of points.

If you don't understand you need to read careful about theory of about KT condition.

Richárd Tóth 2019-8-9