PPD-IPM: Outer primal, inner primal-dual interior-point method for nonlinear programming

TL;DR

This paper introduces a new numerical method for solving nonlinear programming problems that aims to improve convergence and feasibility management over existing algorithms, demonstrated through MATLAB implementation and experiments.

Contribution

A novel primal-dual interior-point method for NLP that overcomes limitations of existing approaches, with proven convergence properties.

Findings

Proven global convergence of the method

Second order local convergence established

Effective performance on large sparse NLPs from optimal control problems

Abstract

In this paper we present a novel numerical method for computing local minimizers of twice smooth differentiable non-linear programming (NLP) problems. So far all algorithms for NLP are based on either of the following three principles: successive quadratic programming (SQP), active sets (AS), or interior-point methods (IPM). Each of them has drawbacks. These are in order: iteration complexity, feasibility management in the sub-program, and utility of initial guesses. Our novel approach attempts to overcome these drawbacks. We provide: a mathematical description of the method; proof of global convergence; proof of second order local convergence; an implementation in \textsc{Matlab}; experimental results for large sparse NLPs from direct transcription of path-constrained optimal control problems.