Open AccessИсчисление касательных и вокруг
Author(s) -
A.G. Kusraev,
S.S. Kutateladze
Publication year - 2018
Publication title -
vladikavkazskij matematičeskij žurnal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.126
H-Index - 2
eISSN - 1814-0807
pISSN - 1683-3414
DOI - 10.23671/vnc.2018.4.9165
Subject(s) - tangent , calculus (dental) , interpretation (philosophy) , set (abstract data type) , calculus of variations , stability (learning theory) , mathematics , limiting , range (aeronautics) , computer science , mathematical optimization , geometry , mathematical analysis , engineering , medicine , mechanical engineering , dentistry , machine learning , programming language , aerospace engineering
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.