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Vector Optimization and Monotone Operators via Convex Duality

Recent Advances

  • Book
  • © 2015

Overview

Authors:
  1. Sorin-Mihai Grad

    1. Faculty of Mathematics, TU Chemnitz, Chemnitz, Germany

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  • Presents the first approach to the maximal monotonicity of the diagonal operators by means of representative functions
  • Introduces a framework for vector duality via general scalarizations
  • Investigates the structure of the closedness-type regularity conditions in scalar optimization, showing how one can derive them

Part of the book series: Vector Optimization (VECTOROPT)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xvii
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  2. Introduction and Preliminaries

    • Sorin-Mihai Grad
    Pages 1-11

  3. Duality for Scalar Optimization Problems

    • Sorin-Mihai Grad
    Pages 13-38

  4. Minimality Concepts for Sets

    • Sorin-Mihai Grad
    Pages 39-59

  5. Vector Duality via Scalarization for Vector Optimization Problems

    • Sorin-Mihai Grad
    Pages 61-113

  6. General Wolfe and Mond-Weir Duality

    • Sorin-Mihai Grad
    Pages 115-175

  7. Vector Duality for Linear and Semidefinite Vector Optimization Problems

    • Sorin-Mihai Grad
    Pages 177-221

  8. Monotone Operators Approached via Convex Analysis

    • Sorin-Mihai Grad
    Pages 223-256

  9. Back Matter

    Pages 257-269
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Keywords

About this book

This book investigates several duality approaches for vector optimization problems, while also comparing them. Special attention is paid to duality for linear vector optimization problems, for which a vector dual that avoids the shortcomings of the classical ones is proposed. Moreover, the book addresses different efficiency concepts for vector optimization problems. Among the problems that appear when the framework is generalized by considering set-valued functions, an increasing interest is generated by those involving monotone operators, especially now that new methods for approaching them by means of convex analysis have been developed. Following this path, the book provides several results on different properties of sums of monotone operators.

Authors and Affiliations

  • Faculty of Mathematics, TU Chemnitz, Chemnitz, Germany

    Sorin-Mihai Grad

About the author

Sorin-Mihai Grad is currently working within the Faculty of Mathematics of Chemnitz University of Technology, Germany, where he achieved his PhD in 2006 and his Habilitation in 2014. He is co-author of the book "Duality in Vector Optimization" (Springer, 2009).

Bibliographic Information

  • Book Title: Vector Optimization and Monotone Operators via Convex Duality

  • Book Subtitle: Recent Advances

  • Authors: Sorin-Mihai Grad

  • Series Title: Vector Optimization

  • DOI: https://doi.org/10.1007/978-3-319-08900-3

  • Publisher: Springer Cham

  • eBook Packages: Business and Economics, Business and Management (R0)

  • Copyright Information: Springer International Publishing Switzerland 2015

  • Hardcover ISBN: 978-3-319-08899-0Published: 17 September 2014

  • Softcover ISBN: 978-3-319-36190-1Published: 23 August 2016

  • eBook ISBN: 978-3-319-08900-3Published: 03 September 2014

  • Series ISSN: 1867-8971

  • Series E-ISSN: 1867-898X

  • Edition Number: 1

  • Number of Pages: XVII, 269

  • Topics: Operations Research/Decision Theory, Optimization, Continuous Optimization

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