Redundancy in Semidefinite Programming

The author introduces and addresses the problem of redundancy in semidefinite programming. This work is motivated by the increasing interest in semidefinite programming and the associated demand for ways of eliminating redundant linear matrix inequality constraints in large semidefinite programming problems. This book develops different techniques for identifying nonredundant and eliminating redundant linear matrix inequality constraints. It discusses both probabilistic and deterministic methods. The first probabilistic method, called the semidefinite-stand-hit method (SSH), applies to general linear matrix inequality constraints and extends the stand-and-hit (SH) method of linear programming. The author also extends the Hypersphere Direction (HD) and the Coordinate Direction (CD) probabilistic methods for linear constraints to linear matrix inequalities. The deterministic methods given apply to diagonalizable linear matrix inequalities and system of ellipsoids. The book is suitable for both graduate students and researchers in operations research.