Tight coefficients of averaged operators via scaled relative graph

Many iterative methods in optimization are fixed-point iterations with averaged operators. As such methods converge at an O(1/k) rate with the constant determined by the averagedness coefficient, establishing small averagedness coefficients for operators is of broad interest. In this paper, we show...

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Veröffentlicht in:	Journal of mathematical analysis and applications 2020-10, Vol.490 (1), p.124211, Article 124211
Hauptverfasser:	Huang, Xinmeng, Ryu, Ernest K., Yin, Wotao
Format:	Artikel
Sprache:	eng
Schlagworte:	Averaged operator Composition of operators Euclidean geometry Mathematics Mathematics, Applied Nonexpansive operator Physical Sciences Science & Technology Three operators
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container_title	Journal of mathematical analysis and applications
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creator	Huang, Xinmeng Ryu, Ernest K. Yin, Wotao
description	Many iterative methods in optimization are fixed-point iterations with averaged operators. As such methods converge at an O(1/k) rate with the constant determined by the averagedness coefficient, establishing small averagedness coefficients for operators is of broad interest. In this paper, we show that the averagedness coefficients of the composition of averaged operators by Ogura and Yamada (2002) [21] and the three-operator splitting by Davis and Yin (2017) [9] are tight. The analysis relies on the scaled relative graph, a geometric tool recently proposed by Ryu et al. (2019) [25].
doi_str_mv	10.1016/j.jmaa.2020.124211
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subjects	Averaged operator Composition of operators Euclidean geometry Mathematics Mathematics, Applied Nonexpansive operator Physical Sciences Science & Technology Three operators
title	Tight coefficients of averaged operators via scaled relative graph
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