Convergence and rate of convergence of some greedy algorithms in convex optimization

TL;DR

This paper systematically analyzes the convergence properties and rates of approximate greedy algorithms in convex optimization, where evaluations may include errors, highlighting their significance in optimization and approximation theory.

Contribution

It provides a comprehensive study of the convergence and rates of approximate greedy algorithms, emphasizing their importance in convex optimization and approximation theory.

Findings

Convergence of approximate greedy algorithms is established.

Rates of convergence are characterized under various conditions.

Approximate evaluations impact the efficiency of greedy algorithms.

Abstract

The paper gives a systematic study of the approximate versions of three greedy-type algorithms that are widely used in convex optimization. By approximate version we mean the one where some of evaluations are made with an error. Importance of such versions of greedy-type algorithms in convex optimization and in approximation theory was emphasized in previous literature.