Talk page

Title:
Positive semidefinite lifts and factorizations

Speaker:
João Gouveia

Abstract:
Representing polytopes by means of linear matrix inequalities as been a highly successful strategy in combinatorial optimization. Geometrically it corresponds to writing a polytope as the projection of an affine slice of the cone of positive semidefinite (psd) matrices i.e., a spectrahedron. Efforts to understand the theoretical limits of such techniques have connected the existance of such representations to a particular type of matrix factorization, the psd factorization of a nonnegative matrix, and its corresponding notion of psd rank. In this talk we will do a brief survey of the main results in the area, its connections to matrix theory and combinatorics and some of the open problems that remain.

Link:
https://www.msri.org/workshops/813/schedules/22811

Workshop:
MSRI- Introductory Workshop: Geometric and Topological Combinatorics