2018/03/05 by Neuenhofen, Martin
#FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.1803.01829
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 Matlab; experimental results for large sparse NLPs from direct transcription of path-constrained optimal control problems.