Greedy Strategies for Convex Optimization

TL;DR

This paper analyzes two greedy algorithms for approximating the minimum of convex functions in Hilbert spaces, providing convergence rates based on the functions' smoothness and convexity properties.

Contribution

It introduces and analyzes two greedy strategies for convex optimization, establishing convergence rates under specific smoothness and convexity conditions.

Findings

Convergence rates are proven for the proposed algorithms.

Conditions involving modulus of smoothness and convexity are key.

Algorithms effectively approximate minima under these conditions.

Abstract

We investigate two greedy strategies for finding an approximation to the minimum of a convex function $E$ defined on a Hilbert space $H$. We prove convergence rates for these algorithms under suitable conditions on the objective function $E$. These conditions involve the behavior of the modulus of smoothness and the modulus of uniform convexity of $E$.