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CMFD, 2014, Volume 53, Pages 64–132 (Mi cmfd262)  

This article is cited in 8 scientific papers (total in 8 papers)

Introduction to sublinear analysis

I. V. Orlov

Vernadskiy Tavricheskiy National University, Faculty of Mathematics and Informatics

Abstract: Basing on the notion of compact subdifferentials, we develop a subdifferential calculus of the first and the second orders beyond the Taylor expansion and extremum theory. We introduce and investigate a comprehensive class of subsmooth maps such that the constructed theory is applicable to them. We develop a technique to investigate one-dimensional extremal variational problems with subsmooth Lagrangians (including sufficient conditions). A number of examples are considered.

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English version:
Journal of Mathematical Sciences, 2016, 218:4, 430–502

UDC: 517.972+517.982.22

Citation: I. V. Orlov, “Introduction to sublinear analysis”, Proceedings of the Crimean autumn mathematical school-symposium, CMFD, 53, PFUR, M., 2014, 64–132; Journal of Mathematical Sciences, 218:4 (2016), 430–502

Citation in format AMSBIB
\Bibitem{Orl14}
\by I.~V.~Orlov
\paper Introduction to sublinear analysis
\inbook Proceedings of the Crimean autumn mathematical school-symposium
\serial CMFD
\yr 2014
\vol 53
\pages 64--132
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd262}
\transl
\jour Journal of Mathematical Sciences
\yr 2016
\vol 218
\issue 4
\pages 430--502
\crossref{https://doi.org/10.1007/s10958-016-3039-z}


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    This publication is cited in the following articles:
    1. I. Baran, I. Orlov, “Adjoint extremal problem for non-smooth functionals”, 2017 Constructive Nonsmooth Analysis and Related Topics, CNSA 2017, Dedicated to the Memory of V.F. Demyanov, ed. L. Polyakova, IEEE, 23–26  isi
    2. I. V. Orlov, “Subdifferentials via sub-operators”, 2017 Constructive Nonsmooth Analysis and Related Topics, CNSA 2017, Dedicated to the Memory of V.F. Demyanov, ed. L. Polyakova, IEEE, 235–238  isi
    3. F. S. Stonyakin, “Subdifferential calculus in abstract convex cones”, 2017 Constructive Nonsmooth Analysis and Related Topics, CNSA 2017, Dedicated to the Memory of V.F. Demyanov, ed. L. Polyakova, IEEE, 316–319  isi
    4. I. V. Orlov, I. V. Baran, “Introduction to sublinear analysis – 2: symmetric case”, Journal of Mathematical Sciences, 225:2 (2017), 265–321  mathnet  crossref
    5. I. V. Orlov, A. V. Tsygankova, “Multidimensional variational functionals with subsmooth integrands”, Eurasian Math. J., 6:3 (2015), 54–75  mathnet
    6. I. V. Orlov, “Inverse and Implicit Function Theorems in the Class of Subsmooth Maps”, Math. Notes, 99:4 (2016), 619–622  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    7. I. V. Orlov, “Embedding of a Uniquely Divisible Abelian Semigroup In a Convex Cone”, Math. Notes, 102:3 (2017), 361–368  mathnet  crossref  crossref  mathscinet  isi  elib
    8. I. V. Orlov, “The Method of Lagrange Multipliers for the Class of Subsmooth Mappings”, Math. Notes, 103:2 (2018), 323–327  mathnet  crossref  crossref  isi  elib
  • Современная математика. Фундаментальные направления
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