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University of Cambridge > Talks.cam > CUED Control Group Seminars > Matrix Inequalities with Matrix Unknowns

## Matrix Inequalities with Matrix UnknownsAdd to your list(s) Download to your calendar using vCal - Professor Bill Helton (Mathematics Department, UC San Diego)
- Friday 16 April 2010, 14:00-15:00
- Cambridge University Engineering Department, LR6.
If you have a question about this talk, please contact Dr Ioannis Lestas. Linear matrix inequalities LMIs are common in many areas: control systems, combinatorial optimization, statistics, etc. They often have unknowns x= ( x_1, ... ,x_n) with x_j scalars, but in many problems of control, certainly the classical ones, the unknowns enter naturally as matrices. The talk treats several topics involving LMIs with matrix unknowns: A basic question in light of the fact that convexity, a seemingly much weaker condition than being an LMI , guarantees numerical success is:
Can we transform a problem to being convex? LMI domination: L dominates \L means L(x) is positive definite implies \L(x) is positive definite. Checking for domination numerically can be NP hard. However, we relax the problem by insisting on domination whenever the unknowns x_j are matrices. There is an elegant algebraic characterization of relaxed LMI domination and numerical solution is no longer NP hard. Roughly what we observed is that this matrix relaxation corresponds exactly to a very natural procedure in modern in modern functional analysis. This talk is part of the CUED Control Group Seminars series. ## This talk is included in these lists:- Cambridge University Engineering Department, LR6
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