Description

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