solve an inequality with LMI approach

2014 2 1
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更新时间：2014 2 5
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I would like to solve this inequality :
Q*A'+A*Q+L'*B'+B*L < 0

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Amit
Amit 2014-2-1
solve for what? What the variable, what is known?
John D'Errico
John D'Errico 2014-2-1
Obviously, the poster wants to solve for x. Oh, x is not in the equation? So we can choose x=0. Case closed.
Seriously, before you ask a question, think about what you mean by it. What are the unknowns here? What are the knowns? Are they arrays? vectors? Scalars? What size? What do you mean by "solve", as that is not a terribly meaningful thing in terms of an inequality, as there will generally be infinitely many solutions to such a problem.
Once you define your problem, it MIGHT be possible to help you, but until then, impossible. Even then, solving an inequality is, as I said, generally not a well-posed problem.
haifa
haifa 2014-2-4
the variables are the two matrix Q and L: Q: symetric matrix >0 L < 0
Matt J
Matt J 2014-2-4
And the inequality < 0 is element-wise, or is it the positive semi-definite ordering?
haifa
haifa 2014-2-5
Q :is a symetric and semi definite positive L: <0
Matt J
Matt J 2014-2-5
Does L<0 mean that L(i,j)<0 for all i,j ?
haifa
haifa 2014-2-5
no,L is a negativ matrix

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回答（1 个）

Johan Löfberg
Johan Löfberg 2014-2-5
编辑：Johan Löfberg 2014-2-5

1 个投票

With the MATLAB Toolbox YALMIP, and some SDP solver installed (such as SDPT3, SeDuMi, Mosek etc) it would be (you have not clearly said which variables are decision variables, I assume Q (psd) and L (arbitrary))
Q = sdpvar(n,n);
L = sdpvar(m,n,'full');
Constraints = [Q >=0, Q*A'+A*Q+L'*B'+B*L <= 0];
solvesdp(Constraints);
The model is ill-posed though as Q and L arbitrarily close to zero is feasible, which means trouble in practice. Dehomogenioze it, for instance
Constraints = [Q >=0, Q*A'+A*Q+L'*B'+B*L <= -eye(n)];

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haifa
haifa 2014-2-5
I try to find the matrix Q:symetric and semi definite positive, and the negativ matrix L, which satisfy this inequality: Q*A'+A*Q+L'*B'+B*L < 0 knowing that: A=[0 1;0 0];B=[0;1];
haifa
haifa 2014-2-5
I have not this solver SDP

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