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 See more:   <Main>