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Matematicheskie Zametki, 2022, Volume 111, Issue 1, Pages 39–53
DOI: https://doi.org/10.4213/mzm13120
(Mi mzm13120)
 

Sufficient Conditions for a Minimum of a Strongly Quasiconvex Function on a Weakly Convex Set

S. I. Dudov, M. A. Osiptsev

Saratov State University
References:
Abstract: We consider a finite-dimensional minimization problem for a strongly quasiconvex function on a weakly convex set. We obtain sufficient conditions for its solution expressed in terms of the strong quasiconvexity constants of the objective function and the weak convexity of the admissible set of arguments, as well as their local characteristics. We separately consider the case of specifying an admissible set by the Lebesgue set of a weakly convex function. For the case of a differentiable objective function, we establish sufficient conditions for a local minimum, including a “strong” stationarity condition and indicate the radius of the corresponding neighborhood.
Keywords: strongly quasiconvex function, strongly and weakly convex sets and functions, subdifferential, normal cone, sufficient conditions for a minimum, radius of the neighborhood of a local minimum.
Received: 21.04.2021
Revised: 09.08.2021
English version:
Mathematical Notes, 2022, Volume 111, Issue 1, Pages 33–46
DOI: https://doi.org/10.1134/S0001434622010059
Bibliographic databases:
Document Type: Article
UDC: 519.853
Language: Russian
Citation: S. I. Dudov, M. A. Osiptsev, “Sufficient Conditions for a Minimum of a Strongly Quasiconvex Function on a Weakly Convex Set”, Mat. Zametki, 111:1 (2022), 39–53; Math. Notes, 111:1 (2022), 33–46
Citation in format AMSBIB
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\paper Sufficient Conditions for a Minimum of a Strongly Quasiconvex Function on a Weakly Convex Set
\jour Mat. Zametki
\yr 2022
\vol 111
\issue 1
\pages 39--53
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\crossref{https://doi.org/10.4213/mzm13120}
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\jour Math. Notes
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\pages 33--46
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  • https://www.mathnet.ru/eng/mzm13120
  • https://doi.org/10.4213/mzm13120
  • https://www.mathnet.ru/eng/mzm/v111/i1/p39
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    Математические заметки Mathematical Notes
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