Quantitative Strong Convergence for the Hybrid Steepest Descent Method

2016/10/03 by Daniel Körnlein, Körnlein, Daniel · 1 citation
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Fixed Point Theorems Analysis #Logic (math.LO) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1610.00517

openalex publication_date 2016/10/03 · openalex created_date 2016/10/14 · openalex updated_date 2026/07/28

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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• Rate of metastability of an iterative algorithm for quadratic optimization

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