Formulating maximization problem subject to null-space constraint

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.

[Torsten]

P(x) is a matrix ?

[Hirak Basumatary]

Yes, P(x) is a matrix.

[Torsten]

What are the dimensions of H and P(x) ?

[Hirak Basumatary]

P = 6 by 6 matrix.

H = 12 by 6 matrix

[Torsten]

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

[Bruno Luong]

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

Answer 1

[Bruno Luong]

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.