Abstract:
A numerical algorithm for minimizing a convex function on the set-theoretic intersection of a smooth surface and a convex compact set in finite-dimensional Euclidean space is proposed. The idea behind the algorithm is to reduce the original problem to a sequence of convex programming problems. Necessary extremum conditions are studied, and the convergence of the algorithm is analyzed.
Key words:
smooth surface, convex compact set, convex programming problem, projection onto a nonconvex set, necessary conditions for a local minimum, convergence of an algorithm.
Citation:
Yu. A. Chernyaev, “Numerical algorithm for minimizing a convex function on the intersection of a smooth surface and a convex compact set”, Zh. Vychisl. Mat. Mat. Fiz., 59:7 (2019), 1151–1157; Comput. Math. Math. Phys., 59:7 (2019), 1098–1104
\Bibitem{Che19}
\by Yu.~A.~Chernyaev
\paper Numerical algorithm for minimizing a convex function on the intersection of a smooth surface and a convex compact set
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2019
\vol 59
\issue 7
\pages 1151--1157
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\crossref{https://doi.org/10.1134/S0044466919070056}
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\transl
\jour Comput. Math. Math. Phys.
\yr 2019
\vol 59
\issue 7
\pages 1098--1104
\crossref{https://doi.org/10.1134/S0965542519070054}
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Linking options:
https://www.mathnet.ru/eng/zvmmf10922
https://www.mathnet.ru/eng/zvmmf/v59/i7/p1151
This publication is cited in the following 1 articles:
Yu. A. Chernyaev, “Numerical algorithm for solving a class of optimization problems with a constraint in the form of a subset of points of a smooth surface”, Comput. Math. Math. Phys., 62:12 (2022), 2033–2040
Citation in format AMSBIB
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