Download e-book for iPad: Abstract Convex Analysis (Wiley-Interscience and Canadian by Ivan Singer

By Ivan Singer

ISBN-10: 0471160156

ISBN-13: 9780471160151

This e-book examines summary convex research and provides the result of fresh examine, particularly on parametrizations of Minkowski sort dualities and of conjugations of style Lau. It explains the most ideas via instances and precise proofs.

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R is any coupling function, replacing w(x) by ga(x, w). 13).

63), for example, those in which the coupling function ça takes only the values 0 and —oc (related to "quasi-subdifferentials"). 65) the subdifferential of f at x o with respect to the conjugation c(p) (or, briefly, the e(ço)-subdifferential of f at x 0 ), and we will also denote it by acm f (x0). 63)). 47) can be extended to arbitrary dualities A : R x —> R w , yielding a general "Fenchel—Young inequality" with respect to A. Since this definition of a° f (x0) is more technical, we will give it only in Chapter 10.

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Abstract Convex Analysis (Wiley-Interscience and Canadian Mathematics Series of Monographs and Texts) by Ivan Singer

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