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Diskretn. Anal. Issled. Oper., 2018, Volume 25, Number 3, Pages 23–35 (Mi da901)  

Minimizing a symmetric quasiconvex function on a two-dimensional lattice

S. I. Veselov, D. V. Gribanov, N. Yu. Zolotykh, A. Yu. Chirkov

Institute of Information Technology, Mathematics, and Mechanics, Lobachevsky Nizhny Novgorod State University, 23 Gagarin Ave., 603950 Nizhny Novgorod, Russia

Abstract: We consider the minimization problem for a symmetric quasiconvex function defined by an oracle on the set of integer points of a square. We formulate an optimality criterion for the solution, obtain a logarithmic lower bound for the complexity of the problem, and propose an algorithm for which the number of inquiries to the oracle is at most thrice the lower bound. Bibliogr. 14.

Keywords: quasiconvex function, oracle, integer lattice.

Funding Agency Grant Number
Russian Science Foundation 17-11-01336
The authors were supported by the Russian Science Foundation (project no. 17-11-01336).


DOI: https://doi.org/10.17377/daio.2018.25.585

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English version:
Journal of Applied and Industrial Mathematics, 2018, 12:3, 587–594

Document Type: Article
UDC: 519.854
Received: 06.07.2017
Revised: 15.12.2017

Citation: S. I. Veselov, D. V. Gribanov, N. Yu. Zolotykh, A. Yu. Chirkov, “Minimizing a symmetric quasiconvex function on a two-dimensional lattice”, Diskretn. Anal. Issled. Oper., 25:3 (2018), 23–35; J. Appl. Industr. Math., 12:3 (2018), 587–594

Citation in format AMSBIB
\Bibitem{VesGriZol18}
\by S.~I.~Veselov, D.~V.~Gribanov, N.~Yu.~Zolotykh, A.~Yu.~Chirkov
\paper Minimizing a~symmetric quasiconvex function on a~two-dimensional lattice
\jour Diskretn. Anal. Issled. Oper.
\yr 2018
\vol 25
\issue 3
\pages 23--35
\mathnet{http://mi.mathnet.ru/da901}
\crossref{https://doi.org/10.17377/daio.2018.25.585}
\transl
\jour J. Appl. Industr. Math.
\yr 2018
\vol 12
\issue 3
\pages 587--594
\crossref{https://doi.org/10.1134/S199047891803016X}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85052091045}


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