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Gebunden. Condition: New. Contains a chapter on hypertopologies (only one other book on this topic)Author includes exercises, for use as a graduate textOver 45 figures are includedThis book deals mainly with the study of convex functions and their behavior f.
Taschenbuch. Condition: Neu. Convexity and Well-Posed Problems | Roberto Lucchetti | Taschenbuch | CMS Books in Mathematics | xiv | Englisch | 2010 | Springer | EAN 9781441921116 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.
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Published by Springer US, Springer New York, 2010
ISBN 10: 1441921117 ISBN 13: 9781441921116
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book deals mainly with the study of convex functions and their behavior from the point of view of stability with respect to perturbations. We shall consider convex functions from the most modern point of view: a function is de ned to be convex whenever its epigraph, the set of the points lying above the graph, is a convex set. Thus many of its properties can be seen also as properties of a certain convex set related to it. Moreover, we shall consider extended real valued functions, i. e. , functions taking possibly the values and + . The reason for considering the value + is the powerful device of including the constraint set of a constrained minimum problem into the objective function itself (by rede ning it as + outside the constraint set). Except for trivial cases, the minimum value must be taken at a point where the function is not + , hence at a point in the constraint set. And the value is allowed because useful operations, such as the inf-convolution, can give rise to functions valued even when the primitive objects are real valued. Observe that de ning the objective function to be + outside the closed constraint set preserves lower semicontinuity, which is the pivotal and mi- mal continuity assumption one needs when dealing with minimum problems. Variational calculus is usually based on derivatives.
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Published by Springer New York Nov 2005, 2005
ISBN 10: 0387287191 ISBN 13: 9780387287195
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Buch. Condition: Neu. Neuware - This book deals with the study of convex functions and of their behavior from the point of view of stability with respect to perturbations. Convex functions are considered from the modern point of view that underlines the geometrical aspect: thus a function is defined as convex whenever its graph is a convex set.A primary goal of this book is to study the problems of stability and well-posedness, in the convex case. Stability means that the basic parameters of a minimum problem do not vary much if we slightly change the initial data. On the other hand, well-posedness means that points with values close to the value of the problem must be close to actual solutions. In studying this, one is naturally led to consider perturbations of functions and of sets.While there exist numerous classic texts on the issue of stability, there only exists one book on hypertopologies [Beer 1993]. The current book differs from Beer s in that it contains a much more condensed explication of hypertopologies and is intended to help those not familiar with hypertopologies learn how to use them in the context of optimization problems. TOC:Preface.- Convex Sets and Convex Functions: the fundamentals.- Continuity and Gamma (X).- The Derivatives and the Subdifferential.- Minima and Quasi Minima.- The Fenchel Conjugate.- Duality.- Linar Programming and Game Theory.-Hypertopologies, Hyperconvergences.- Continuity of Some Operations Between Functions.- Well-Posed Problems.- Generic Well-Posedness.- More Exercises.- Appendix A: Functional Analysis.- Appendix B: Topology.- Appendix C: More Game Theory.- Appendix D: Symbols, Notations, Definitions and Important Theorems.- References, Index.
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Published by Springer New York Nov 2010, 2010
ISBN 10: 1441921117 ISBN 13: 9781441921116
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book deals mainly with the study of convex functions and their behavior from the point of view of stability with respect to perturbations. We shall consider convex functions from the most modern point of view: a function is de ned to be convex whenever its epigraph, the set of the points lying above the graph, is a convex set. Thus many of its properties can be seen also as properties of a certain convex set related to it. Moreover, we shall consider extended real valued functions, i. e. , functions taking possibly the values and + . The reason for considering the value + is the powerful device of including the constraint set of a constrained minimum problem into the objective function itself (by rede ning it as + outside the constraint set). Except for trivial cases, the minimum value must be taken at a point where the function is not + , hence at a point in the constraint set. And the value is allowed because useful operations, such as the inf-convolution, can give rise to functions valued even when the primitive objects are real valued. Observe that de ning the objective function to be + outside the closed constraint set preserves lower semicontinuity, which is the pivotal and mi- mal continuity assumption one needs when dealing with minimum problems. Variational calculus is usually based on derivatives. 320 pp. Englisch.
Language: English
Published by Springer-Verlag New York Inc., 2005
ISBN 10: 0387287191 ISBN 13: 9780387287195
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Contains a chapter on hypertopologies (only one other book on this topic)Author includes exercises, for use as a graduate textOver 45 figures are includedThis book deals mainly with the study of convex functions and their behavior f.
Language: English
Published by Springer US, Springer New York Nov 2010, 2010
ISBN 10: 1441921117 ISBN 13: 9781441921116
Seller: buchversandmimpf2000, Emtmannsberg, BAYE, Germany
Taschenbuch. Condition: Neu. This item is printed on demand - Print on Demand Titel. Neuware -This book deals mainly with the study of convex functions and their behavior from the point of view of stability with respect to perturbations. We shall consider convex functions from the most modern point of view: a function is de ned to be convex whenever its epigraph, the set of the points lying above the graph, is a convex set. Thus many of its properties can be seen also as properties of a certain convex set related to it. Moreover, we shall consider extended real valued functions, i. e. , functions taking possibly the values and + . The reason for considering the value + is the powerful device of including the constraint set of a constrained minimum problem into the objective function itself (by rede ning it as + outside the constraint set). Except for trivial cases, the minimum value must be taken at a point where the function is not + , hence at a point in the constraint set. And the value is allowed because useful operations, such as the inf-convolution, can give rise to functions valued even when the primitive objects are real valued. Observe that de ning the objective function to be + outside the closed constraint set preserves lower semicontinuity, which is the pivotal and mi- mal continuity assumption one needs when dealing with minimum problems. Variational calculus is usually based on derivatives.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 320 pp. Englisch.