Introduction to Linear Optimization - Arkadi Nemirovski - Bog

The book presents a graduate level, rigorous, and self-contained introduction to linear optimization (LO), the presented topics beingexpressive abilities of LO;
geometry of LO - structure of polyhedral sets, LO duality and its applications;
traditional LO algorithms - primal and dual simplex methods, and network simplex method;
polynomial time solvability of LO via ellipsoid algorithm;
conic programming with emphasis on expressing abilities of second order and semidefinite optimization, and polynomial time primal-dual interior point algorithms for linear and semidefinite optimization.