Nonlinear matrix inequality constraints in fmincon

Hi,

I wish to use 'fmincon' to minimize a linear function subject to nonlinear matrix inequality constraints of the form: L(i) = [gi+x(1) x(2)*x(3); x(2)*x(3) qi+x(4)] >= 0, for all i={1,2,..,n}.

The size of the (symmetric) matrix L(i) can be as large as 7x7.

I have MATLAB v7.5 (release 2007b) and from reading the documentation on fmincon, it appears that the nonlinear constraints can only be vectors. So is there any way to impose nonlinear matrix inequality constraints L(i) >= 0.

Many thanks.

Answer 1

[Matt J]

I'm pretty sure fmincon disregards the shape of the nonlinear constraint array that you supply (since why would the shape matter?). Regardless, there's no clear reason why you have to organize your L(i) as a 7x7 matrix. You can reshape it into a 49x1 vector without changing the meaning of the constraints.