Linear Matrix Inequality (LMI) representation of convex semialgebraic sets
 
 
Description:  Semidefinite programming (SDP) is a powerful new approach in optimization that has blossomed since the mid 1990s. In a SDP problem, we maximize or minimize a linear functional over a convex set in Rd given by

{(x1,...,xd) : A0 + x1 A1 + ... + xd Ad \geq 0},


where A0,A1,...,Ad are real symmetric matrices of some size, and the inequality means that a real symmetric matrix is positive semidefinite. Notice that the classical linear programming (LP) is a very special case when the matrices A0,A1,...,Ad commute hence are simultaneously diagonalizable. This leads to the question: which convex semialgebraic sets in Rd can be represented as above (such a representation is called a LMI representation)? I will describe some of the work done over the last decade on this and related questions.
Date:  2011-02-23
Start Time:   11:30
Speaker:  Victor Vinnikov (Ben Gurion University, Israel)
Institution:  -
Place:  Room 5.5
Research Groups: -Algebra and Combinatorics
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