Abstract:
A numerical algorithm for minimizing a convex function on the set-theoretic intersection of a spherical surface and a convex compact set is proposed. The idea behind the algorithm is to reduce the original minimization problem to a sequence of convex programming problems. Necessary extremum conditions are examined, and the convergence of the algorithm is analyzed.
Key words:
spherical surface, convex compact set, convex programming problem, necessary conditions for a local minimum, convergence of an algorithm.
Citation:
Yu. A. Chernyaev, “Iterative algorithm for minimizing a convex function at the intersection of a spherical surface and a convex compact set”, Zh. Vychisl. Mat. Mat. Fiz., 57:10 (2017), 1631–1640; Comput. Math. Math. Phys., 57:10 (2017), 1607–1615
\Bibitem{Che17}
\by Yu.~A.~Chernyaev
\paper Iterative algorithm for minimizing a convex function at the intersection of a spherical surface and a convex compact set
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2017
\vol 57
\issue 10
\pages 1631--1640
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\crossref{https://doi.org/10.7868/S0044466917100064}
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\jour Comput. Math. Math. Phys.
\yr 2017
\vol 57
\issue 10
\pages 1607--1615
\crossref{https://doi.org/10.1134/S0965542517100062}
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Linking options:
https://www.mathnet.ru/eng/zvmmf10623
https://www.mathnet.ru/eng/zvmmf/v57/i10/p1631
This publication is cited in the following 2 articles:
A. M. Dulliev, “Minimizatsiya gladkoi funktsii na granitse vneshnego obobschennogo segmenta sfery”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2024, no. 87, 22–33
Yu. A. Chernyaev, “Numerical algorithm for minimizing a convex function on the intersection of a smooth surface and a convex compact set”, Comput. Math. Math. Phys., 59:7 (2019), 1098–1104
Citation in format AMSBIB
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