Titlebook: Convex Analysis and Beyond; Volume I: Basic Theo Boris S. Mordukhovich,Nguyen Mau Nam Textbook 2022 Springer Nature Switzerland AG 2022 Top

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CONVEXIFIED LIPSCHITZIAN ANALYSIS,way are always ., but the most important properties of them are exhibited when the directional derivatives are assumed (or happen to be) . with respect to directions. All of this constitutes the realm of . in this chapter.

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Textbook 2022 convex, Banach and finite-dimensional settings. These developments and expositions are based on the powerful geometric approach of variational analysis, which resides on set extremality with its characterizations and specifications in the presence of convexity. Using this approach, the text consoli

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VARIATIONAL TECHNIQUES AND FURTHER SUBGRADIENT STUDY,r functions in convex analysis. Our major results hold in Banach spaces, but some results and proofs are valid in general settings of complete metric and topological vector spaces, while those for spectral and singular functions are primarily finite-dimensional.

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https://doi.org/10.1057/9781137349927of convex functions. Further topics on convexity, including duality and generalized differentiation theories, are considered in the subsequent chapters. Unless otherwise stated, we consider . in this chapter and the subsequent ones.

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Shahira Fahmy,Mary Angela Bock,Wayne Wanta but also sets with nonsmooth boundaries as well as set-valued mappings. . of generalized differentiation have been the central issue of the theory and applications from the very beginning of convex analysis.

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Why Macroprudential Policy? Brief Overviewway are always ., but the most important properties of them are exhibited when the directional derivatives are assumed (or happen to be) . with respect to directions. All of this constitutes the realm of . in this chapter.

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CONVEX GENERALIZED DIFFERENTIATION,s are nondifferentiable at the points of interest, the now flourishing generalized differentiation theory oriented toward optimization-related problems has started from convex analysis and then has been extended to more general variational frameworks. It concerns not only nondifferentiable functions