Abstract:
The minimization of a smooth functional on a generalized spherical segment of a finite-dimensional Euclidean space is examined. A relaxation method that involves successive projections of the antigradient onto auxiliary sets of a simpler structure is proposed. It is shown that, under certain natural assumptions, this method converges to a stationary point.
Citation:
A. M. Dulliev, “A relaxation method for minimizing a smooth function on a generalized spherical segment”, Zh. Vychisl. Mat. Mat. Fiz., 54:2 (2014), 208–223; Comput. Math. Math. Phys., 54:2 (2014), 219–234
\Bibitem{Dul14}
\by A.~M.~Dulliev
\paper A relaxation method for minimizing a smooth function on a generalized spherical segment
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2014
\vol 54
\issue 2
\pages 208--223
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\crossref{https://doi.org/10.7868/S0044466914020045}
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\transl
\jour Comput. Math. Math. Phys.
\yr 2014
\vol 54
\issue 2
\pages 219--234
\crossref{https://doi.org/10.1134/S0965542514020043}
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Linking options:
https://www.mathnet.ru/eng/zvmmf9988
https://www.mathnet.ru/eng/zvmmf/v54/i2/p208
This publication is cited in the following 5 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
Yu. A. Chernyaev, “Convergence of the gradient projection method and Newton's method as applied to optimization problems constrained by intersection of a spherical surface and a convex closed set”, Comput. Math. Math. Phys., 56:10 (2016), 1716–1731
A. M. Dulliev, “Nearly optimal coverings of a sphere with generalized spherical segments”, Comput. Math. Math. Phys., 55:7 (2015), 1110–1119
Yu. A. Chernyaev, “An extension of the gradient projection method and Newton's method to extremum problems constrained by a smooth surface”, Comput. Math. Math. Phys., 55:9 (2015), 1451–1460
Citation in format AMSBIB
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