Journal of Convex Analysis 28 (2021), No. 3, [final page numbers not yet available]
Copyright Heldermann Verlag 2021
Quantitative Results on the Multi-Parameters Proximal Point Algorithm
Departamento de MatemŠtica, Faculdade de Ciencias, Universidade de Lisboa, Portugal
Department of Mathematics, Technische Universitšt, 64289 Darmstadt, Germany
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.
Keywords: Maximal monotone operator, proximal point algorithm, metastability, asymptotic regularity, proof mining.
MSC: 47H09, 47N10, 03F10, 46S30.
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