Introduction to Linear Optimization

The book presents a graduate level, rigorous, and self-contained introduction to linear optimization (LO), the presented topics being expressive 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.;