An inexact potential reduction method for linear programming

TL;DR

This paper introduces an inexact potential reduction method for linear programming that improves robustness and maintains convergence guarantees by controlling solution errors in interior point methods.

Contribution

It reformulates the linear system in interior point methods to be less sensitive to perturbations and develops implementable error control conditions.

Findings

Maintains convergence and complexity bounds with inexact directions.

Provides a reformulation of the linear system for robustness.

Develops practical error control conditions.

Abstract

A class of interior point methods using inexact directions is analysed. The linear system arising in interior point methods for linear programming is reformulated such that the solution is less sensitive to perturbations in the right-hand side. For the new system an implementable condition is formulated that controls the relative error in the solution. Based on this condition, a feasible and an infeasible potential reduction method are described which retain the convergence and complexity bounds known for exact directions.