English

Quantitative Strong Convergence for the Hybrid Steepest Descent Method

Logic 2016-10-04 v1

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.

Keywords

Cite

@article{arxiv.1610.00517,
  title  = {Quantitative Strong Convergence for the Hybrid Steepest Descent Method},
  author = {Daniel Körnlein},
  journal= {arXiv preprint arXiv:1610.00517},
  year   = {2016}
}
R2 v1 2026-06-22T16:08:42.059Z