Introduction to Linear Optimization

Arkadi Nemirovski

• 25 januari 2024
• 9789811277924

Samenvatting:

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