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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 attemptsarXiv:1803.01829v1 fatcat:khw2ryagzjh53ih3e2allo5s6e