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

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 $\text{textsc}Matlab$; experimental results for large sparse NLPs from direct transcription of path-constrained optimal control problems.