Quantitative Strong Convergence for the Hybrid Steepest Descent Method

Daniel Körnlein

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arXiv · 1610.00517

Quantitative Strong Convergence for the Hybrid Steepest Descent Method

Daniel Körnlein

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Abstract

We provide new complexity information for the convergence of the Hybrid Steepest Descent Method for solving the Variational Inequality Problem for a strict contraction on Hilbert space over a closed convex set C given either as the fixed point set of a single nonexpansive mapping or the intersection of the fixed point sets of a finite family of nonexpansive mappings. More precisely, we give metastability rates in the sense of Tao for those cases. The results in this paper were extracted from a proof due to Yamada using proof-mining techniques, and provide a thorough quantitative analysis of the Hybrid Steepest Descent Method.

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BibTeX RIS

Daniel Körnlein. 2016-10-03. Quantitative Strong Convergence for the Hybrid Steepest Descent Method. https://arxiv.org/abs/1610.00517

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