Titlebook: Constructive Nonsmooth Analysis and Related Topics; Vladimir F. Demyanov,Panos M. Pardalos,Mikhail Bat Book 2014 Springer Science+Business

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Fuzzy Multidimensional DatabasesConsider the problem of the best approximate separation of two finite sets in the linear case. This problem is reduced to the problem of nonsmooth optimization, analyzing which we use all power of the linear programming theory. Ideologically we follow Bennett and Mangassarian (Optim. Meth. Software 1, 23–34 1992).

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https://doi.org/10.1007/978-3-642-10663-7As a new illustration of the versatility of abstract subdifferentials we examine their introduction in the field of analysis of second-order generalized derivatives. We also consider some calculus rules for some of the various notions of such derivatives and we give an account of the effect of the Moreau regularization process.

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Use Model Theory in Nonsmooth Analysis,This is a short invitation to using the models of nonstandard set theory in nonsmooth analysis. The techniques of the infinitesimal and Boolean-valued versions of analysis are illustrated by the concept of infinitesimal optimality and the operator-valued Farkas lemma.

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