Convex Matrix Inequalities vs Linear Matrix Inequalities

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• Professor Bill Helton (Mathematics Department, University of California San Diego)
• Monday 16 June 2008, 11:30-12:30
• Cambridge University Engineering Department, Lecture Room 4.

If you have a question about this talk, please contact Dr Guy-Bart Stan.

A substantial advance in optimization starting in the 1990’s was the realization that problems in many areas, like linear system control, combinatorics, statistics convert directly to matrix inequalities, abbreviated MIs, of which by dent of great cleverness some convert to Linear Matrix Inequalities, LMI ’s. A basic question is: which Matrix Inequalities are in fact Linear Matrix Inequalities? Clearly, LMIs are convex, but what about the converse?

How much more restricted are LMIs than Convex MIs?

There is getting to be a reasonable road map to this problem with much left to be proved. It involves use and development of techniques from areas like functional analysis, real algebraic geometry (polynomial inequalities) and matrix theory. In this talk we give results and conjectures on the answer to the LMI vs convexity question.

This talk is part of the CUED Control Group Seminars series.

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