Formulating maximization problem subject to null-space constraint

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Hirak Basumatary 2019-7-2

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评论： Bruno Luong 2019-7-2

I have a maximization problem subjected to a null-space constraint in the form:

Q = max f(x);

subject to: Nullspace(P(x)*H') = 0

Here, 'x' is the independent variable. 'P' is dependent on 'x' and is a matrix. 'H' is a constant matrix.

How can i formulate this optimization problem in MATLAB ? Using 'fmincon' it seems not possible because the equality constraint is a matrix.

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Torsten 2019-7-2

Then P*H' is 6x12, and the nullspace can never be 0.

Bruno Luong 2019-7-2

Exact. One more reason why the problem as stated is meaningless

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Bruno Luong 2019-7-2

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编辑：Bruno Luong 2019-7-2

FMINCON (or any optimizer) cannot solve this kind of problem, your asmmissible space is not close set, since the constraint can be written as abs(smallest eigen values) > 0.

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