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Introduction to Linear Optimization

Compare Textbook Prices for Introduction to Linear Optimization  ISBN 9789811277900 by Arkadi Nemirovski
Author: Arkadi Nemirovski
ISBN:9811277907
ISBN-13: 9789811277900
List Price: $144.90 (up to 0% savings)
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Details about 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

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With over 30 years of teaching, I have the honor and pleasure to say that I have former students – who are doctors, scientists, Engineers, and business men & women - who still keep in touch and even come to visit. Some keep in-touch even from other countries and many call or Skype; and some call for help and advice. Read more

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