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Generalized Preinvexity and Second Order Duality in Multiobjective Programming

  • Book
  • © 2018

Overview

Authors:
  1. Xinmin Yang

    1. College of Mathematics Science, Chongqing Normal University, Chongqing, China

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  • Introduces generalized convex functions and generalized monotone functions
  • Equips readers with generalized preinvex functions and generalized invariant monotonicities
  • Application to the study of optimality conditions and duality theory in optimization

Part of the book series: Springer Optimization and Its Applications (SOIA, volume 142)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xii
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  2. Generalized Preinvexity

    1. Front Matter

      Pages 1-1
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    2. Preinvex Functions

      • Xinmin Yang
      Pages 3-20

    3. Semistrictly Preinvex Functions

      • Xinmin Yang
      Pages 21-41

    4. Semipreinvex Functions

      • Xinmin Yang
      Pages 43-52

    5. Prequasiinvex Functions

      • Xinmin Yang
      Pages 53-74

  3. Generalized Invariant Monotonicity

    1. Front Matter

      Pages 75-75
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    2. Generalized Invexity and Generalized Invariant Monotonicity

      • Xinmin Yang
      Pages 77-91

  4. Duality in Multiobjective Programming

    1. Front Matter

      Pages 93-93
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    2. Multiobjective Wolfe Type Second-Order Symmetric Duality

      • Xinmin Yang
      Pages 95-107

    3. Multiobjective Mond-Weir-Type Second-Order Symmetric Duality

      • Xinmin Yang
      Pages 109-120

    4. Multiobjective Second-Order Duality with Cone Constraints

      • Xinmin Yang
      Pages 121-148

    5. Multiobjective Higher-Order Duality

      • Xinmin Yang
      Pages 149-158

  5. Back Matter

    Pages 159-167
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Keywords

About this book

This book introduces readers to several new generalized preinvex functions and generalized invariant monotone functions. It begins by describing the main properties of these functions and various relations. Several examples are then presented to illustrate various interesting relationships among preinvex functions and the properly inclusive relations among the generalized invariant monotonicities. In addition, several second order and higher order symmetric duality models are provided for multi-objective nonlinear programming problems. Lastly, weak and strong duality theorems under generalized convexity assumptions are provided.

The book offers a well-synthesized, accessible, and usable treatment for students, researchers and practitioners in the areas of OR, optimization, applied mathematics and engineering, and all those working on a wide range of related problems, which include financial institutions, logistics, transportation, traffic management, etc.


Authors and Affiliations

  • College of Mathematics Science, Chongqing Normal University, Chongqing, China

    Xinmin Yang

Bibliographic Information

  • Book Title: Generalized Preinvexity and Second Order Duality in Multiobjective Programming

  • Authors: Xinmin Yang

  • Series Title: Springer Optimization and Its Applications

  • DOI: https://doi.org/10.1007/978-981-13-1981-5

  • Publisher: Springer Singapore

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Singapore Pte Ltd. 2018

  • Hardcover ISBN: 978-981-13-1980-8Published: 10 October 2018

  • Softcover ISBN: 978-981-13-4715-3Published: 01 February 2019

  • eBook ISBN: 978-981-13-1981-5Published: 27 September 2018

  • Series ISSN: 1931-6828

  • Series E-ISSN: 1931-6836

  • Edition Number: 1

  • Number of Pages: XII, 167

  • Number of Illustrations: 4 b/w illustrations

  • Topics: Operations Research, Management Science, Real Functions

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