PPD-IPM: Outer primal, inner primal-dual interior-point method for nonlinear programming
This work proposes a novel algorithmic framework for nonlinear programming, potentially improving iteration complexity, feasibility management, and initial guess utility for practitioners solving large-scale NLPs.
The paper introduces a new interior-point method for nonlinear programming that combines outer primal and inner primal-dual steps, aiming to overcome drawbacks of SQP, active set, and existing interior-point methods. It provides convergence proofs and demonstrates effectiveness on large sparse optimal control problems.
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.