A. V. Arutyunov, S. E. Zhukovskiy, K. V. Storozhuk, “The structure of the set of local minima of functions in various spaces”, Sibirsk. Mat. Zh., 2019, Volume 60, Number 3,Pages <nobr>518–526</nobr>

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Sibirsk. Mat. Zh., 2019 Volume 60, Number 3, Pages 518–526 (Mi smj3092)

The structure of the set of local minima of functions in various spaces

A. V. Arutyunov^abc, S. E. Zhukovskiy^bcd, K. V. Storozhuk^ef

^a Kharkevich Institute for Information Transmission Problems, Moscow, Russia
^b Trapeznikov Institute of Control Sciences, Moscow, Russia
^c Peoples' Friendship University of Russia, Moscow, Russia
^d Moscow Institute of Physics and Technology, Moscow, Russia
^e Sobolev Institute of Mathematics, Novosibirsk, Russia
^f Novosibirsk State University, Novosibirsk, Russia

Abstract: We study the topological properties and cardinalities of the sets of strict local minima of functions on $f$-quasimetric and topological spaces.

Keywords: $f$-quasimetric space, local minimum of a function.

UDC: 517.988.38

Received: 15.07.2018
Revised: 09.01.2019
Accepted: 12.03.2019

DOI: 10.33048/smzh.2019.60.304

English version: Siberian Mathematical Journal, 2019, 60:3, 398–404

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© Steklov Math. Inst. of RAS, 2024