Directional descent

TL;DR

This paper identifies the optimal descent direction for convex functions and develops an algorithm capable of minimizing certain non-convex functions by leveraging this direction.

Contribution

It introduces a method to find the best descent direction for convex functions and extends it to minimize some non-convex functions.

Findings

Optimal descent direction for convex functions identified

Algorithm successfully minimizes a subset of non-convex functions

Theoretical guarantees provided for the proposed method

Abstract

We identity the optimal non-infinitesimal direction of descent for a convex function. An algorithm is developed that can theoretically minimize a subset of (non-convex) functions.