ISSN 1683-3414 (Print)   •   ISSN 1814-0807 (Online)
   Log in
 

Contacts

Address: Vatutina st. 53, Vladikavkaz,
362025, RNO-A, Russia
Phone: (8672)23-00-54
E-mail: rio@smath.ru

 

 

 

яндекс.ћетрика

DOI: 10.23671/VNC.2018.4.9165

Calculus of Tangents and Beyond

Kusraev, A. G. , Kutateladze, S. S.
Vladikavkaz Mathematical Journal 2017. Vol. 19. Issue 4.
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.
Keywords: Hadamard cone, Bouligand cone, Clarke cone, general position, operator inequality, Boolean valued analysis, nonstandard analysis
Language: English Download the full text  
For citation: Kusraev A. G., Kutateladze S. S. Calculus of Tangents and Beyond // Vladikavkazskii matematicheskii †zhurnal [Vladikavkaz Math. J.], 2017, vol. 19, no. 1, pp. 27-34. DOI 10.23671/VNC.2018.4.9165
+ References


← Contents of issue
 
  | Home | Editorial board | Publication ethics | Peer review guidelines | Current | Archive | Rules for authors | Send an article |  
© 1999-2023 ёжный математический институт