2019•arXiv (Cornell University)Open access

Stability of KKT systems and superlinear convergence of the SQP method\n under parabolic regularity

Ashkan Mohammadi, Boris S. Mordukhovich, Ebrahim Sarabi

Abstract

This paper pursues a two-fold goal. Firstly, we aim to derive novel\nsecond-order characterizations of important robust stability properties of\nperturbed Karush-Kuhn-Tucker systems for a broadclass of constrained\noptimization problems generated by parabolically regular sets. Secondly, the\nobtained characterizations are applied to establish well-posedness and\nsuperlinear convergence of the basic sequential quadratic programming method to\nsolve parabolically regular constrained optimization problems.\n

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Key concepts: Karush–Kuhn–Tucker conditions, Sequential quadratic programming, Mathematics, Convergence (economics), Stability (learning theory), Mathematical optimization, Quadratic programming, Constrained optimization problem