An optimal variant of Kelley's cutting-plane method

TL;DR

This paper introduces a new variant of Kelley's cutting-plane method that achieves the optimal convergence rate for minimizing nonsmooth convex Lipschitz functions, enhancing efficiency in convex optimization.

Contribution

The paper presents a novel, constructively derived variant of Kelley's method with proven optimal convergence rates for nonsmooth convex optimization.

Findings

Achieves optimal convergence rate for nonsmooth convex functions

Constructively derived variant of Kelley's method

Proven theoretical efficiency improvements

Abstract

We propose a new variant of Kelley's cutting-plane method for minimizing a nonsmooth convex Lipschitz-continuous function over the Euclidean space. We derive the method through a constructive approach and prove that it attains the optimal rate of convergence for this class of problems.