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Vladikavkaz. Mat. Zh., 2017, Volume 19, Number 4, Pages 27–34 (Mi vmj630)  

Calculus of tangents and beyond

A. G. Kusraevab, S. S. Kutateladzec

a North Ossetian State University, 44-46 Vatutin Street, Vladikavkaz, 362025, Russia
b Vladikavkaz Science Center of the RAS, 22 Markus Street, Vladikavkaz, 362027, Russia
c Sobolev Institute of Mathematics, 4 Acad. Koptyug avenue, Novosibirsk, 630090, Russia

Abstract: Optimization is the choice of what is most preferable. Geometry and local analysis of nonsmooth objects are needed for variational analysis which embraces optimization. These involved admissible directions and tangents as the limiting positions of the former. The calculus of tangents is one of the main techniques of optimization. Calculus reduces forecast to numbers, which is scalarization in modern parlance. Spontaneous solutions are often labile and rarely optimal. Thus, optimization as well as calculus of tangents deals with inequality, scalarization and stability. The purpose of this article is to give an overview of the modern approach to this range of questions based on non-standard models of set theory. A model of a mathematical theory is usually called nonstandard if the membership within the model has interpretation different from that of set theory. In the recent decades much research is done into the nonstandard methods located at the junctions of analysis and logic. This area requires the study of some new opportunities of modeling that open broad vistas for consideration and solution of various theoretical and applied problems.

Key words: Hadamard cone, Bouligand cone, Clarke cone, general position, operator inequality, Boolean valued analysis, nonstandard analysis.

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UDC: 517.982.252
Received: 15.08.2017
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Citation: A. G. Kusraev, S. S. Kutateladze, “Calculus of tangents and beyond”, Vladikavkaz. Mat. Zh., 19:4 (2017), 27–34

Citation in format AMSBIB
\Bibitem{KusKut17}
\by A.~G.~Kusraev, S.~S.~Kutateladze
\paper Calculus of tangents and beyond
\jour Vladikavkaz. Mat. Zh.
\yr 2017
\vol 19
\issue 4
\pages 27--34
\mathnet{http://mi.mathnet.ru/vmj630}


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