Rescaled Pure Greedy Algorithm for Convex Optimization

TL;DR

This paper introduces a new greedy algorithm for convex optimization in Banach spaces, demonstrating its convergence rates based on the smoothness properties of the objective function.

Contribution

It proposes a novel rescaled pure greedy algorithm with proven convergence rates tailored for convex optimization in Banach spaces.

Findings

Convergence rates depend on the modulus of uniform smoothness.

The algorithm is effective for convex functions with specific smoothness properties.

Provides theoretical guarantees for the proposed greedy strategy.

Abstract

We suggest a new greedy strategy for convex optimization in Banach spaces and prove its convergent rates under a suitable behavior of the modulus of uniform smoothness of the objective function.