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Normal Numbers and Pseudorandom Generators Kapitel lesen Erstes Kapitel lesen

2013 | OriginalPaper | Buchkapitel

10. Compactness, Optimality, and Risk

verfasst von : B. Cascales, J. Orihuela, M. Ruiz Galán

Erschienen in: Computational and Analytical Mathematics

Verlag: Springer New York

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Abstract

This is a survey about one of the most important achievements in optimization in Banach space theory, namely, James’ weak compactness theorem, its relatives, and its applications. We present here a good number of topics related to James’ weak compactness theorem and try to keep the technicalities needed as simple as possible: Simons’ inequality is our preferred tool. Besides the expected applications to measures of weak noncompactness, compactness with respect to boundaries, size of sets of norm-attaining functionals, etc., we also exhibit other very recent developments in the area. In particular we deal with functions and their level sets to study a new Simons’ inequality on unbounded sets that appear as the epigraph of some fixed function f. Applications to variational problems for f and to risk measures associated with its Fenchel conjugate f ∗ are studied.

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Vorheriges Kapitel Monotone Operator Methods for Nash Equilibria in Non-potential Games
Nächstes Kapitel Logarithmic and Complex Constant Term Identities
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Metadaten
Titel
Compactness, Optimality, and Risk
verfasst von
B. Cascales
J. Orihuela
M. Ruiz Galán
Copyright-Jahr
2013
Verlag
Springer New York
Buch
Computational and Analytical Mathematics

Print ISBN: 978-1-4614-7620-7

Electronic ISBN: 978-1-4614-7621-4

Copyright-Jahr: 2013

DOI
https://doi.org/10.1007/978-1-4614-7621-4_10