Abstract:
We propose a method of bi-coordinate variations for optimal resource allocation problems, which involve simplex type constraints. It consists in making coordinate-wise steps together with special threshold control and tolerances whose values reduce sequentially. The method is simpler essentially than the usual gradient ones, which enables one to apply it to large dimensional optimization problems. We establish its convergence and rate of convergence under rather mild assumptions.
Citation:
I. V. Konnov, “A method of bi-coordinate variations with tolerances and its convergence”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 1, 80–85; Russian Math. (Iz. VUZ), 60:1 (2016), 68–72
\Bibitem{Kon16}
\by I.~V.~Konnov
\paper A method of bi-coordinate variations with tolerances and its convergence
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2016
\issue 1
\pages 80--85
\mathnet{http://mi.mathnet.ru/ivm9072}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2016
\vol 60
\issue 1
\pages 68--72
\crossref{https://doi.org/10.3103/S1066369X16010084}
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https://www.mathnet.ru/eng/ivm9072
https://www.mathnet.ru/eng/ivm/y2016/i1/p80
This publication is cited in the following 6 articles:
I. V. Konnov, “Selective bi-coordinate method for limit non-smooth resource allocation type problems”, Set-Valued Var. Anal., 27:1 (2019), 191–211
I Konnov, O Pinyagina, “Selective bi-coordinate variations without line-search”, J. Phys.: Conf. Ser., 1158 (2019), 032016
O. V. Pinyagina, “Metod pokoordinatnogo spuska dlya zadachi rynochnogo ravnovesiya s tsenovymi gruppami”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 160, no. 4, Izd-vo Kazanskogo un-ta, Kazan, 2018, 718–730
Igor Konnov, Olga Pinyagina, Springer Proceedings in Mathematics & Statistics, 247, Computational Aspects and Applications in Large-Scale Networks, 2018, 161
Verdyck J., Blondia Ch., Moonen M., “Derivative Based Real-Time Spectrum Coordination For Dsl”, 2016 24Th European Signal Processing Conference (Eusipco), European Signal Processing Conference, IEEE, 2016, 305–309
Jeroen Verdyck, Chris Blondia, Marc Moonen, 2016 24th European Signal Processing Conference (EUSIPCO), 2016, 305
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