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Record Nr. |
UNINA9910300260403321 |
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Autore |
Khan Akhtar A |
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Titolo |
Set-valued Optimization : An Introduction with Applications / / by Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu |
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Pubbl/distr/stampa |
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Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2015 |
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ISBN |
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Edizione |
[1st ed. 2015.] |
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Descrizione fisica |
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1 online resource (781 p.) |
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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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Mathematical optimization |
Operations research |
Decision making |
Management science |
Game theory |
Optimization |
Operations Research/Decision Theory |
Continuous Optimization |
Operations Research, Management Science |
Game Theory, Economics, Social and Behav. Sciences |
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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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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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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Sommario/riassunto |
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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. |
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