Set-valued optimization : an introduction with applications

著者

    • Khan, Akhtar A.
    • Tammer, Christiane
    • Zălinescu, C.

書誌事項

Set-valued optimization : an introduction with applications

Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu

(Vector optimization)

Springer, c2015

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注記

Includes bibliographical references (p. 733-758) and indexes

内容説明・目次

内容説明

Set-valued optimization is a vibrant and expanding branch of mathematics that deals with optimization problems where the objective map and/or the constraints maps are set-valued maps acting between certain spaces. Since set-valued maps subsumes single valued maps, set-valued optimization provides an important extension and unification of the scalar as well as the vector optimization problems. Therefore this relatively new discipline has justifiably attracted a great deal of attention in recent years. This book presents, in a unified framework, basic properties on ordering relations, solution concepts for set-valued optimization problems, a detailed description of convex set-valued maps, most recent developments in separation theorems, scalarization techniques, variational principles, tangent cones of first and higher order, sub-differential of set-valued maps, generalized derivatives of set-valued maps, sensitivity analysis, optimality conditions, duality and applications in economics among other things.

目次

Introduction.- Order Relations and Ordering Cones.- Continuity and Differentiability.- Tangent Cones and Tangent Sets.- Nonconvex Separation Theorems.- Hahn-Banach Type Theorems.- Hahn-Banach Type Theorems.- Conjugates and Subdifferentials.- Duality.- Existence Results for Minimal Points.- Ekeland Variational Principle.- Derivatives and Epiderivatives of Set-valued Maps.- Optimality Conditions in Set-valued Optimization.- Sensitivity Analysis in Set-valued Optimization and Vector Variational Inequalities.- Numerical Methods for Solving Set-valued Optimization Problems.- Applications.

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詳細情報

  • NII書誌ID(NCID)
    BB17152503
  • ISBN
    • 9783642542640
  • 出版国コード
    gw
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Berlin
  • ページ数/冊数
    xxii, 765 p.
  • 大きさ
    25 cm
  • 分類
  • 件名
  • 親書誌ID
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