Convergence Analysis of an Inexact Feasible Interior Point Method for Convex Quadratic Programming

TL;DR

This paper analyzes two variants of an inexact feasible interior point method for convex quadratic programming, focusing on convergence, error tolerance, and complexity for short-step and long-step algorithms.

Contribution

It introduces and analyzes two inexact feasible interior point algorithms with different neighborhood structures and establishes their convergence and complexity bounds.

Findings

Both algorithms allow inexact solutions to Newton systems.

Conditions for acceptable inexactness are provided.

Worst-case complexity results are established for both methods.

Abstract

In this paper we will discuss two variants of an inexact feasible interior point algorithm for convex quadratic programming. We will consider two different neighbourhoods: a (small) one induced by the use of the Euclidean norm which yields a short-step algorithm and a symmetric one induced by the use of the infinity norm which yields a (practical) long-step algorithm. Both algorithms allow for the Newton equation system to be solved inexactly. For both algorithms we will provide conditions for the level of error acceptable in the Newton equation and establish the worst-case complexity results.