Quantitative results on the multi-parameters Proximal Point Algorithm

arXiv1912.10175MaRDI QIDQ6331565

Publication date: 19 December 2019

Abstract: We give a quantitative analysis of a theorem due to Fenghui Wang and Huanhuan Cui concerning the convergence of a multi-parametric version of the proximal point algorithm. Wang and Cui's result ensures the convergence of the algorithm to a zero of the operator. Our quantitative analysis provides explicit bounds on the metastability (in the sense of Terence Tao) for the convergence and the asymptotic regularity of the iteration. Moreover, our analysis bypasses the need of sequential weak compactness and only requires a weak form of the metric projection argument.

Mathematics Subject Classification ID

Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Applications of operator theory in optimization, convex analysis, mathematical programming, economics (47N10) Functionals in proof theory (03F10) Constructive functional analysis (46S30)

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