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Vector variational inequalities and ...

Ansari, Qamrul Hasan.

Vector variational inequalities and vector optimizationtheory and applications /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Vector variational inequalities and vector optimizationby Qamrul Hasan Ansari, Elisabeth Kobis, Jen-Chih Yao.
其他題名:	theory and applications /
作者:	Ansari, Qamrul Hasan.
其他作者:	Kobis, Elisabeth.
出版者:	Cham :Springer International Publishing :2018.
面頁冊數:	xiii, 509 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Variational inequalities (Mathematics)
電子資源:	http://dx.doi.org/10.1007/978-3-319-63049-6
ISBN:	9783319630496$q(electronic bk.)

Vector variational inequalities and vector optimizationtheory and applications /
Ansari, Qamrul Hasan.

Vector variational inequalities and vector optimizationtheory and applications /[electronic resource] :by Qamrul Hasan Ansari, Elisabeth Kobis, Jen-Chih Yao. - Cham :Springer International Publishing :2018. - xiii, 509 p. :ill., digital ;24 cm. - Vector optimization,1867-8971. - Vector optimization..

Preliminaries -- Analysis over Cones -- Solution Concepts in Vector Optimization -- Classical Methods in Vector Optimization -- Vector Variational Inequalities -- Linear Scalarization of Vector Variational Inequalities -- Nonsmooth Vector Variational Inequalities -- Generalized Vector Variational Inequalities -- Vector Equilibrium Problems -- Generalized Vector Equilibrium Problems.

This book presents the mathematical theory of vector variational inequalities and their relations with vector optimization problems. It is the first-ever book to introduce well-posedness and sensitivity analysis for vector equilibrium problems. The first chapter provides basic notations and results from the areas of convex analysis, functional analysis, set-valued analysis and fixed-point theory for set-valued maps, as well as a brief introduction to variational inequalities and equilibrium problems. Chapter 2 presents an overview of analysis over cones, including continuity and convexity of vector-valued functions. The book then shifts its focus to solution concepts and classical methods in vector optimization. It describes the formulation of vector variational inequalities and their applications to vector optimization, followed by separate chapters on linear scalarization, nonsmooth and generalized vector variational inequalities. Lastly, the book introduces readers to vector equilibrium problems and generalized vector equilibrium problems. Written in an illustrative and reader-friendly way, the book offers a valuable resource for all researchers whose work involves optimization and vector optimization.

ISBN: 9783319630496$q(electronic bk.)

Standard No.: 10.1007/978-3-319-63049-6doiSubjects--Topical Terms:

185202
Variational inequalities (Mathematics)

LC Class. No.: QA316

Dewey Class. No.: 515.64

Vector variational inequalities and vector optimizationtheory and applications /
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505 0 $a Preliminaries -- Analysis over Cones -- Solution Concepts in Vector Optimization -- Classical Methods in Vector Optimization -- Vector Variational Inequalities -- Linear Scalarization of Vector Variational Inequalities -- Nonsmooth Vector Variational Inequalities -- Generalized Vector Variational Inequalities -- Vector Equilibrium Problems -- Generalized Vector Equilibrium Problems.
520 $a This book presents the mathematical theory of vector variational inequalities and their relations with vector optimization problems. It is the first-ever book to introduce well-posedness and sensitivity analysis for vector equilibrium problems. The first chapter provides basic notations and results from the areas of convex analysis, functional analysis, set-valued analysis and fixed-point theory for set-valued maps, as well as a brief introduction to variational inequalities and equilibrium problems. Chapter 2 presents an overview of analysis over cones, including continuity and convexity of vector-valued functions. The book then shifts its focus to solution concepts and classical methods in vector optimization. It describes the formulation of vector variational inequalities and their applications to vector optimization, followed by separate chapters on linear scalarization, nonsmooth and generalized vector variational inequalities. Lastly, the book introduces readers to vector equilibrium problems and generalized vector equilibrium problems. Written in an illustrative and reader-friendly way, the book offers a valuable resource for all researchers whose work involves optimization and vector optimization.
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