Abstract:
The distance from a given point to the solution set of a system of strict and nonstrict inequalities described by convex functions is estimated. As consequences, estimates for the distance from a given point to the Lebesgue set of a convex function are obtained and sufficient conditions for convex-valued set-valued mappings to be covering are established.
Key words:
convex functions, systems of convex inequalities, estimates for distances to a set.
Citation:
A. V. Arutyunov, S. E. Zhukovskiy, “On estimates for solutions of systems of convex inequalities”, Zh. Vychisl. Mat. Mat. Fiz., 55:9 (2015), 1486–1492; Comput. Math. Math. Phys., 55:9 (2015), 1444–1450
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\by A.~V.~Arutyunov, S.~E.~Zhukovskiy
\paper On estimates for solutions of systems of convex inequalities
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2015
\vol 55
\issue 9
\pages 1486--1492
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\crossref{https://doi.org/10.7868/S0044466915070030}
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\jour Comput. Math. Math. Phys.
\yr 2015
\vol 55
\issue 9
\pages 1444--1450
\crossref{https://doi.org/10.1134/S0965542515070039}
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Linking options:
https://www.mathnet.ru/eng/zvmmf10261
https://www.mathnet.ru/eng/zvmmf/v55/i9/p1486
This publication is cited in the following 2 articles:
Jelena Vicanovic, “Optimality conditions for isoperimetric continuous - time optimization problems”, Yugosl J Oper Rres, 33:2 (2023), 249
V. V. Voloshinov, “A generalization of the Karush–Kuhn–Tucker theorem for approximate solutions of mathematical programming problems based on quadratic approximation”, Comput. Math. Math. Phys., 58:3 (2018), 364–377
Citation in format AMSBIB
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