Rate of metastability of an iterative algorithm for quadratic optimization

TL;DR

This paper uses proof mining techniques to quantitatively analyze the metastability rate of an iterative algorithm solving quadratic optimization problems, providing explicit convergence and regularity rates.

Contribution

It offers the first quantitative, proof-mining-based analysis of convergence rates for an iterative quadratic optimization algorithm.

Findings

Established quadratic rates of asymptotic regularity for specific sequences

Derived explicit rates of metastability and asymptotic regularity

Enhanced understanding of convergence behavior in quadratic optimization algorithms

Abstract

In this paper, relying on methods from proof mining, we provide a quantitative analysis of a theorem due to Xu, stating that an iteration strongly converges to the solution of a well known quadratic optimization problem. Rates of metastability and some rates of asymptotic regularity were obtained. We get quadratic rates of asymptotic regularity for particular sequences.