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Record Nr. |
UNINA9910298169903321 |
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Autore |
Ansari Qamrul Hasan |
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Titolo |
Vector Variational Inequalities and Vector Optimization : Theory and Applications / / by Qamrul Hasan Ansari, Elisabeth Köbis, Jen-Chih Yao |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018 |
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ISBN |
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Edizione |
[1st ed. 2018.] |
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Descrizione fisica |
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1 online resource (XIII, 509 p. 60 illus., 1 illus. in color.) |
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Collana |
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Vector Optimization, , 1867-8971 |
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Disciplina |
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Soggetti |
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Operations research |
Decision making |
Mathematical optimization |
Calculus of variations |
Management science |
Operations Research/Decision Theory |
Continuous Optimization |
Calculus of Variations and Optimal Control; Optimization |
Operations Research, Management Science |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references at the end of each chapters and index. |
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Nota di contenuto |
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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. |
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Sommario/riassunto |
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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 |
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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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