Weak and strong convergence of generalized proximal point algorithms with relaxed parameters

Hui Ouyang ()
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Hui Ouyang: University of British Columbia

Journal of Global Optimization, 2023, vol. 85, issue 4, No 8, 969-1002

Abstract: Abstract In this work, we propose and study a framework of generalized proximal point algorithms associated with a maximally monotone operator. We indicate sufficient conditions on the regularization and relaxation parameters of generalized proximal point algorithms for the equivalence of the boundedness of the sequence of iterations generated by this algorithm and the non-emptiness of the zero set of the maximally monotone operator, and for the weak and strong convergence of the algorithm. Our results cover or improve many results on generalized proximal point algorithms in our references. Improvements of our results are illustrated by comparing our results with related known ones.

Keywords: Proximal point algorithm; Maximally monotone operators; Resolvent; Firmly nonexpansiveness; Weak convergence; Strong convergence; Primary 65J15; 47J25; 47H05; Secondary 90C25; 90C30 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10898-022-01241-0

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