Stable interior-point method for convex quadratic programming with strict error bounds

TL;DR

This paper introduces a stable short step interior-point method for convex quadratic programming that guarantees weak polynomial time complexity and numerical stability without strict assumptions on problem feasibility or conditioning.

Contribution

It presents a novel interior-point algorithm applicable to a broad class of nonlinear problems, with proven stability and efficiency guarantees.

Findings

Method has weak polynomial time complexity

Provides a complete proof of numerical stability

Handles infeasible problems by finding interior least-squares solutions

Abstract

We present a short step interior point method for solving a class of nonlinear programming problems with quadratic objective function. Convex quadratic programming problems can be reformulated as problems in this class. The method is shown to have weak polynomial time complexity. A complete proof of the numerical stability of the method is provided. No requirements on feasibility, row-rank of the constraint Jacobian, strict complementarity, or conditioning of the problem are made. Infeasible problems are solved to an optimal interior least-squares solution.