Conical averagedness and convergence analysis of fixed point algorithms

Sedi Bartz (), Minh N. Dao () and Hung M. Phan ()
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Sedi Bartz: University of Massachusetts Lowell
Minh N. Dao: Federation University Australia
Hung M. Phan: University of Massachusetts Lowell

Journal of Global Optimization, 2022, vol. 82, issue 2, No 7, 373 pages

Abstract: Abstract We study a conical extension of averaged nonexpansive operators and the role it plays in convergence analysis of fixed point algorithms. Various properties of conically averaged operators are systematically investigated, in particular, the stability under relaxations, convex combinations and compositions. We derive conical averagedness properties of resolvents of generalized monotone operators. These properties are then utilized in order to analyze the convergence of the proximal point algorithm, the forward–backward algorithm, and the adaptive Douglas–Rachford algorithm. Our study unifies, improves and casts new light on recent studies of these topics.

Keywords: Adaptive Douglas–Rachford algorithm; Cocoercivity; Conically averaged operator; Forward–backward algorithm; Proximal point algorithm; Strong monotonicity; Weak monotonicity; Primary: 47H10; 49M27; Secondary: 65K05; 65K10 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10898-021-01057-4

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