On the Linear Convergence of the Cauchy Algorithm for a Class of Restricted Strongly Convex Functions

TL;DR

This paper extends the linear convergence proof of the Cauchy algorithm from smooth strongly convex functions to a broader class of restricted strongly convex functions, enhancing understanding of its efficiency.

Contribution

It generalizes the convergence results of the Cauchy algorithm to include restricted strongly convex functions, broadening its theoretical applicability.

Findings

Proves linear convergence for a new class of functions

Extends previous results to restricted strongly convex functions

Provides theoretical foundation for algorithm efficiency

Abstract

In this short note, we extend the linear convergence result of the Cauchy algorithm, derived recently by E. Klerk, F. Glineur, and A. Taylor, from the case of smooth strongly convex functions to the case of restricted strongly convex functions with certain form.