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Uspekhi Mat. Nauk, 1970, Volume 25, Issue 1(151), Pages 57–112 (Mi umn5294)  

This article is cited in 3 scientific papers (total in 3 papers)

The general theory of relaxation processes for convex functionals

Yu. I. Lyubich, G. D. Maistrovskii


Abstract: This article sets out a theory of the convergence of minimization processes convex functionals that reduce the value of the functional at each step. A geometrical language, independent of the algorithmic structure, is used to describe the processes: the language of relaxation angles and factors. Convergence conditions are derived and the rate of convergence and stability of the process are studied in this terminology. Translation from the language of concrete algorithms to the geometrical terminology is not difficult, and thanks to this the theory has a wide area of applications: gradient and operator-gradient processes, processes of Newtonian type, coordinate relaxation, Jacobi processes and relaxation for the Rayleigh functional.

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English version:
Russian Mathematical Surveys, 1970, 25:1, 57–117

Bibliographic databases:

UDC: 517.948+519.9
MSC: 52A41, 41A25
Received: 29.06.1969

Citation: Yu. I. Lyubich, G. D. Maistrovskii, “The general theory of relaxation processes for convex functionals”, Uspekhi Mat. Nauk, 25:1(151) (1970), 57–112; Russian Math. Surveys, 25:1 (1970), 57–117

Citation in format AMSBIB
\Bibitem{LyuMai70}
\by Yu.~I.~Lyubich, G.~D.~Maistrovskii
\paper The general theory of relaxation processes for convex functionals
\jour Uspekhi Mat. Nauk
\yr 1970
\vol 25
\issue 1(151)
\pages 57--112
\mathnet{http://mi.mathnet.ru/umn5294}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=266016}
\zmath{https://zbmath.org/?q=an:0202.42202|0207.45001}
\transl
\jour Russian Math. Surveys
\yr 1970
\vol 25
\issue 1
\pages 57--117
\crossref{https://doi.org/10.1070/RM1970v025n01ABEH001255}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. L. V. Kantorovich, “Methods of optimization and mathematical models in economics”, Russian Math. Surveys, 25:5 (1970), 105–107  mathnet  crossref  mathscinet  zmath
    2. I. Ya. Zabotin, “On the stability of algorithms for the unconditional minimization of pseudoconvex functions”, Russian Math. (Iz. VUZ), 44:12 (2000), 31–46  mathnet  mathscinet  zmath  elib
    3. Bunich, AL, “Synthesis of discrete systems: Certain nonstandard problems”, Automation and Remote Control, 61:6 (2000), 994  mathnet  mathscinet  zmath  isi
  • Успехи математических наук Russian Mathematical Surveys
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