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Subdifferentials

Theory and Applications
BuchKartoniert, Paperback
405 Seiten
Englisch
Springer Netherlandserschienen am13.10.2012Softcover reprint of the original 1st ed. 1995
To this end, consider an abstract minimization problem formulated as follows: x E X, f(x) --+ inf. In these circumstances, we are usually interested in the quantity inf f( x), the value of the problem, and in a solution or an optimum plan of the problem (i.mehr
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Produkt

KlappentextTo this end, consider an abstract minimization problem formulated as follows: x E X, f(x) --+ inf. In these circumstances, we are usually interested in the quantity inf f( x), the value of the problem, and in a solution or an optimum plan of the problem (i.
Details
ISBN/GTIN978-94-010-4117-1
ProduktartBuch
EinbandartKartoniert, Paperback
Erscheinungsjahr2012
Erscheinungsdatum13.10.2012
AuflageSoftcover reprint of the original 1st ed. 1995
ReiheMathematics and Its Applications
Seiten405 Seiten
SpracheEnglisch
Gewicht660 g
IllustrationenIX, 405 p.
Artikel-Nr.30370494

Inhalt/Kritik

Inhaltsverzeichnis
1. Convex Correspondences and Operators.- 1. Convex Sets.- 2. Convex Correspondences.- 3. Convex Operators.- 4. Fans and Linear Operators.- 5. Systems of Convex Objects.- 6. Comments.- 2. Geometry of Subdifferentials.- 1. The Canonical Operator Method.- 2. Extremal Structure of Subdifferentials.- 3. Subdifferentials of Operators Acting in Modules.- 4. The Intrinsic Structure of Subdifferentials.- 5. Caps and Faces.- 6. Comments.- 3. Convexity and Openness.- 1. Openness of Convex Correspondences.- 2. The Method of General Position.- 3. Calculus of Polars.- 4. Dual Characterization of Openness.- 5. Openness and Completeness.- 6. Comments.- 4. The Apparatus of Subdifferential Calculus.- 1. The Young-Fenchel Transform.- 2. Formulas for Subdifferentiation.- 3. Semicontinuity.- 4. Maharam Operators.- 5. Disintegration.- 6. Infinitesimal Sub differentials.- 7. Comments.- 5. Convex Extremal Problems.- 1. Vector Programs. Optimality.- 2. The Lagrange Principle.- 3. Conditions for Optimality and Approximate Optimality.- 4. Conditions for Infinitesimal Optimality.- 5. Existence of Generalized Solutions.- 6. Comments.- 6. Local Convex Approximations.- 1. Classification of Local Approximations.- 2. Kuratowski and Rockafellar Limits.- 3. Approximations Determined by a Set of Infinitesimals.- 4. Approximation to the Composition of Sets.- 5. Subdifferentials of Nonsmooth Operators.- 6. Comments.- References.- Author Index.- Symbol Index.mehr