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

Contents:

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  Preface

  
  


• 
  

  About the Author

  
  


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  Main Notational Conventions

  
  


• 
  

  Introduction to LO: Examples of LO Models

  
  


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  Geometry of Linear Optimization:

  
  
  
  
  • Polyhedral Sets and their Geometry
  
  
  • Theory of Systems of Linear Inequalities and Duality
  
  
  
  


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  Classical Algorithms of Linear Optimization: The Simplex Method:

  
  
  
  
  • Simplex Method
  
  
  • The Network Simplex Algorithm
  
  
  
  


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  Complexity of Linear Optimization and the Ellipsoid Method:

  
  
  
  
  • Polynomial Time Solvability of Linear Optimization
  
  
  
  


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  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
  
  
  
  


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  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