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Mat. Zametki, 2019, Volume 105, Issue 3, Pages 406–420 (Mi mz11902)  

Methods for solving ill-posed extremum problems with optimal and extra-optimal quality

A. S. Leonov

National Engineering Physics Institute "MEPhI", Moscow

Abstract: The concept of the quality of approximate solutions of ill-posed extremum problems is introduced and a posteriori quality estimates for various solution methods are studied. Examples of quality functionals are given, which can be used to solve practical extremum problems. New concepts of optimal, optimal in order and extra-optimal quality of the method for solving the extremum problem are determined. The theory of stable methods for solving extremum problems (regularizing algorithms) with optimal order and extra optimal quality is developed, in which, in particular, the property of consistency of the evaluation function of quality is studied. Examples of regularizing algorithms with extra-optimal quality of solutions for extremal problems are given.

Keywords: ill-posed extremum problems, regularizing algorithms, quality of approximate solution, a posteriori estimate of quality, regularizing algorithm of extra-optimal quality.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-01-00159-a
17-51-53002-ГФЕН-а
Ministry of Education and Science of the Russian Federation 02.a03.21.0005
This work was supported by the Russian Foundation for Basic Research under grants 17-01-00159-a and 17-51-53002-GFEN-a and by the Programm for Increasing the Competitive Position of National Research Nuclear University “MEPhI” (Moscow Engineering-Physical Institute) under grant no. 02.a03.21.0005, August 27, 2013.


DOI: https://doi.org/10.4213/mzm11902

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Document Type: Article
UDC: 517.972
Received: 19.12.2017
Revised: 03.03.2018

Citation: A. S. Leonov, “Methods for solving ill-posed extremum problems with optimal and extra-optimal quality”, Mat. Zametki, 105:3 (2019), 406–420

Citation in format AMSBIB
\Bibitem{Leo19}
\by A.~S.~Leonov
\paper Methods for solving ill-posed extremum problems with optimal and extra-optimal quality
\jour Mat. Zametki
\yr 2019
\vol 105
\issue 3
\pages 406--420
\mathnet{http://mi.mathnet.ru/mz11902}
\crossref{https://doi.org/10.4213/mzm11902}
\elib{http://elibrary.ru/item.asp?id=37045127}


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