INTRODUCTION TO LINEAR OPTIMIZATION

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

Contents:

• Preface
• About the Author
• Main Notational Conventions
• Introduction to LO: Examples of LO Models
• Geometry of Linear Optimization:
  • Polyhedral Sets and their Geometry
  • Theory of Systems of Linear Inequalities and Duality
• Classical Algorithms of Linear Optimization: The Simplex Method:
  • Simplex Method
  • The Network Simplex Algorithm
• Complexity of Linear Optimization and the Ellipsoid Method:
  • Polynomial Time Solvability of Linear Optimization
• Conic Programming and Interior Point Methods:
  • Conic Programming
  • Interior Point Methods for LO and Semidefinite Optimization
• Appendices:
  • Prerequisites from Linear Algebra
  • Prerequisites from Real Analysis
  • Symmetric Matrices
• Bibliography
• Solutions to Selected Exercises
• Index

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