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

Coralia Cartis, N. I. M. Gould, Philippe Toint

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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.

langue originaleAnglais
Pages (de - à)68-94
Nombre de pages32
journalJournal of Complexity
Les DOIs
Etat de la publicationPublié - 10 août 2019

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