Optimality of orders one to three and beyond: characterization and evaluation complexity in constrained nonconvex optimization

C. Cartis; N. I. M. Gould; Ph. L. Toint

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arXiv · 1705.07285

Optimality of orders one to three and beyond: characterization and evaluation complexity in constrained nonconvex optimization

C. Cartis·N. I. M. Gould·Ph. L. Toint

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Abstract

Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second- and third-order criticality and its evaluation complexity is analyzed as a function of the choice (among existing methods) of an inner algorithm for solving subproblems in each of the two phases. The relation between high-order criticality and penalization techniques is finally considered, showing that standard algorithmic approaches will fail if approximate constrained high-order critical points are sought.

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C. Cartis, N. I. M. Gould, Ph. L. Toint. 2017-05-20. Optimality of orders one to three and beyond: characterization and evaluation complexity in constrained nonconvex optimization. https://arxiv.org/abs/1705.07285

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