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Multiobjective Linear Programming

An Introduction

  • Textbook
  • © 2016

Overview

Authors:
  1. Dinh The Luc

    1. Avignon University, Avignon, France

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  • Provides an accessible introduction to the field of multiobjective optimization
  • Begins with an elementary and concise review of the mathematical backgrounds
  • Presents basic notions and advanced developments in the field, amply illustrated with computational examples
  • Includes three popular methods for solving multiobjective linear programs: the multiobjective simplex method, normal direction method and outcome space method
  • Includes supplementary material: sn.pub/extras

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xii
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  2. Introduction

    • Dinh The Luc
    Pages 1-3

  3. Background

    1. Front Matter

      Pages 5-5
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    2. Convex Polyhedra

      • Dinh The Luc
      Pages 7-48

    3. Linear Programming

      • Dinh The Luc
      Pages 49-82

  4. Theory

    1. Front Matter

      Pages 83-83
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    2. Pareto Optimality

      • Dinh The Luc
      Pages 85-118

    3. Duality

      • Dinh The Luc
      Pages 119-182

    4. Sensitivity and Stability

      • Dinh The Luc
      Pages 183-237

  5. Methods

    1. Front Matter

      Pages 239-239
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    2. Multiobjective Simplex Method

      • Dinh The Luc
      Pages 241-260

    3. Normal Cone Method

      • Dinh The Luc
      Pages 261-287

    4. Outcome Space Method

      • Dinh The Luc
      Pages 289-307

  6. Back Matter

    Pages 309-325
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Keywords

About this book

This book introduces the reader to the field of multiobjective optimization through problems with simple structures, namely those in which the objective function and constraints are linear. Fundamental notions as well as state-of-the-art advances are presented in a comprehensive way and illustrated with the help of numerous examples. Three of the most popular methods for solving multiobjective linear problems are explained, and exercises are provided at the end of each chapter, helping students to grasp and apply key concepts and methods to more complex problems. The book was motivated by the fact that the majority of the practical problems we encounter in management science, engineering or operations research involve conflicting criteria and therefore it is more convenient to formulate them as multicriteria optimization models, the solution concepts and methods of which cannot be treated using traditional mathematical programming approaches.

Reviews

“The purpose of this book is to introduce readers to the field of multiobjective optimization using problems with fairly simple structures, namely those in which the objective and constraint functions are linear. … The book is pleasant to read, and contains numerical examples for illustration. The book can be used in the first part of a course on multiobjective optimization for undergraduates or first-year graduate students in applied mathematics, engineering, computer science, operations research, and economics.” (I. M. Stancu-Minasian, Mathematical Reviews, April, 2016)

Authors and Affiliations

  • Avignon University, Avignon, France

    Dinh The Luc

About the author

Dinh The Luc is Distinguished Professor, Director of the Laboratory of Mathematics at Avignon University. He is also Research Fellow of the Vietnam Academy of Science and Technology. He was graduated from Lomonosov Moscow State University in 1974 and received his PhD from the Hungarian Academy of Sciences in 1983. His research interests center on vector optimization, nonsmooth analysis, set-valued analysis and multi-criteria transportation network. His monograph "Theory of Vector Optimization" published by Springer in 1989 is one of the most cited books in this area. He is also co-author with V. Jeyakumar of "Nonsmooth Vector Functions and Continuous Optimization" (Springer 2008).

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