Journal of Convex Analysis 28 (2021), No. 3, 729--750
Copyright Heldermann Verlag 2021
Quantitative Results on the Multi-Parameters Proximal Point Algorithm
Bruno Dinis
Departamento de Matemática, Faculdade de Ciencias, Universidade de Lisboa, Portugal
bmdinis@fc.ul.pt
Pedro Pinto
Department of Mathematics, Technische Universität, 64289 Darmstadt, Germany
pinto@mathematik.tu-darmstadt.de
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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