A Unified Approach to Convex and Convexified Generalized Differentiation of Nonsmooth Functions and Set-Valued Mappings

The primary goal of this paper is to present a unified approach and shed new light on convex and Clarke generalized differentiation theories using the concepts and techniques from Mordukhovich’s developments. We show that the concepts and techniques used by Mordukhovich are important, not only to hi...

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Vydáno v:Vietnam journal of mathematics Ročník 42; číslo 4; s. 479 - 497
Hlavní autoři: Nam, Nguyen Mau, Hoang, Nguyen Dinh, Rector, R. Blake
Médium: Journal Article
Jazyk:angličtina
Vydáno: Singapore Springer Singapore 01.12.2014
Témata:
Mathematics
Mathematics and Statistics
90C31
Subgradient
49J53
49J52
Subdifferential
Coderivative
Generalized differentiation
ISSN:2305-221X, 2305-2228
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Shrnutí:The primary goal of this paper is to present a unified approach and shed new light on convex and Clarke generalized differentiation theories using the concepts and techniques from Mordukhovich’s developments. We show that the concepts and techniques used by Mordukhovich are important, not only to his generalized differentiation theory itself, but also to many other aspects of nonsmooth analysis. In particular, they can be used to derive convex subdifferential calculus rules as well as many important calculus rules of Clarke subdifferentials.
ISSN:2305-221X
2305-2228
DOI:10.1007/s10013-014-0073-3