9781441921116 - Convexity and Well-posed Problems (cms Books in Mathematics) by Lucchetti, Roberto (15 results)
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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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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: pr…eigu.
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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.
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Condition: New. Print on Demand pp. 320 46 Illus.
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Condition: New. PRINT ON DEMAND pp. 320.
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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 t…heir behavior f.
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Taschenbuch. Condition: Neu. This item is printed on demand - Print on Demand Titel. Neuware -This book studies the problems of stability and well-posedness, in the convex case. Stability means the basic parameters of a minimum problem do not vary much if we slightly change the initial data, while well-posedness means points wit…h 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.This book contains a 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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 320 pp. Englisch.
