INTRODUCTION TO LINEAR OPTIMIZATION

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

Contents:
PrefaceAbout the AuthorMain Notational ConventionsIntroduction to LO: Examples of LO ModelsGeometry of Linear Optimization:Polyhedral Sets and their GeometryTheory of Systems of Linear Inequalities and DualityClassical Algorithms of Linear Optimization: The Simplex Method:Simplex MethodThe Network Simplex AlgorithmComplexity of Linear Optimization and the Ellipsoid Method:Polynomial Time Solvability of Linear OptimizationConic Programming and Interior Point Methods:Conic ProgrammingInterior Point Methods for LO and Semidefinite OptimizationAppendices:Prerequisites from Linear AlgebraPrerequisites from Real AnalysisSymmetric MatricesBibliographySolutions to Selected ExercisesIndex
Readership: Senior undergraduate and graduate students dealing with building and processing optimizaiton models. Main textbook for a semester-long graduate course on linear optimization; auxiliary text for more general graduate courses on optimization.

Key Features: Linear optimization has wide application in decision making, engineering, and data science The author is a renowned expert on the topic Self-contained with background information summarized in the appendices Rigorous presentation of all the essential but avoid heavy technical detail wherever possible Novel approach or results: (1) presenting "calculus" of problems reducible to LO (something which traditionally is taught via a sample of instructive examples) including, in particular, the results on polynomial time reducibility of Conic Quadratic Optimization to LO; (2) Another novelty is in presenting the basic theory of contemporary extension of LO — Conic Programming, primarily, Conic Quadratic and Semidefinite Optimization, with emphasis on expressive abilities of these generic problems and on Conic Programming Duality; (3) In addition, we describe basic versions of polynomial time primal-dual path-following algorithms for LO and SDO and carry out rigorous complexity analysis of these algorithms