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
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About the Author
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Main Notational Conventions
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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
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Appendices:
- Prerequisites from Linear Algebra
- Prerequisites from Real Analysis
- Symmetric Matrices
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Bibliography
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Solutions to Selected Exercises
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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
