Enhanced Basic Procedures for the Projection and Rescaling Algorithm

TL;DR

This paper introduces three improved versions of the Projection and Rescaling algorithm's basic procedures, leveraging an efficient implementation of Caratheodory's theorem to achieve better complexity than previous methods.

Contribution

The paper presents novel enhanced procedures for the Projection and Rescaling algorithm that improve computational complexity using an efficient Caratheodory's theorem implementation.

Findings

Each enhanced procedure has better complexity order than previous versions.

The methods demonstrate improved efficiency in algorithmic implementation.

The approach advances the theoretical understanding of projection and rescaling algorithms.

Abstract

Using an efficient algorithmic implementation of Caratheodory's theorem, we propose three enhanced versions of the Projection and Rescaling algorithm's basic procedures each of which improves upon the order of complexity of its analogue in [Mathematical Programming Series A, 166 (2017), pp. 87-111].