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How to solve LMIs with equality constraints using MATLAB?

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David Cho
David Cho 2018-1-16
编辑： Frank 2018-11-25
Hi
I would like to find n by n matrices P and Q that minimize
*J = norm(P) + w*norm(Q), where w is a given weight,
subject to
P>=0, Q>=0, and f(P,Q)=0, where f(P,Q)=0 is a given function of P and Q.*
I tried to solve this problem using the lmi solver of MATLAB, but have no idea how to deal with the equality constraint: f(P,Q)=0.
f(P,Q)=0 is equivalent to f(P,Q)>=0 and f(P,Q)<=0, but MATLAB only solves strictly feasible constraints.
But the above problem contains not strictly feasible constraints.
Is there any good solution to handle this kind of problem using MATLAB?
Thank you.
  2 个评论
David Cho
David Cho 2018-1-17
Torsten - Thank you for your comment.
How can we use 'fmincon' for multiple decision variables (P and Q)?
Also, in this problem the decision variables are matrices.

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回答（1 个）

Frank
Frank 2018-11-25
编辑：Frank 2018-11-25
Section 2.5 of Byod's book Linear Matrix Inequalities in System and Control Theory specifically talks about this problem.

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