Use Model Theory in Nonsmooth Analysis

Kutateladze, S. S.

doi:10.1007/978-1-4614-8615-2_1

S. S. Kutateladze⁵

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 87))

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Abstract

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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Notes

1.
Cp. [1, Theorem 4.2.8].
2.
Cp. [3, Sect. 5.7].
3.
Cp. [1, p. 51].
4.
Cp. [7].
5.
Cp. [5].
6.
Letter of April 29, 2009 to S. S. Kutateladze.
7.
Cp. [4]
8.
Cp. [7, p. 349].

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Authors and Affiliations

Sobolev Institute of Mathematics, 4 Koptuyg Avenue, Novosibirsk, 630090, Russia
S. S. Kutateladze

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S. S. Kutateladze
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Correspondence to S. S. Kutateladze .

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Editors and Affiliations

Saint Petersburg State University, Saint Petersburg, Russia
Vladimir F. Demyanov
Department of Industrial & Systems Engin, University of Florida, Gainesville, Florida, USA
Panos M. Pardalos
Higher School of Economics, National Research University, Nizhny Novgorod, Russia
Mikhail Batsyn

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Kutateladze, S.S. (2014). Use Model Theory in Nonsmooth Analysis. In: Demyanov, V., Pardalos, P., Batsyn, M. (eds) Constructive Nonsmooth Analysis and Related Topics. Springer Optimization and Its Applications, vol 87. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8615-2_1

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DOI: https://doi.org/10.1007/978-1-4614-8615-2_1
Published: 26 September 2013
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-8614-5
Online ISBN: 978-1-4614-8615-2
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