Optimality of orders one to three and beyond: characterization and evaluation complexity in constrained nonconvex optimization
Optimization and Control
2021-05-31 v2 Computational Complexity
Numerical Analysis
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.
Cite
@article{arxiv.1705.07285,
title = {Optimality of orders one to three and beyond: characterization and evaluation complexity in constrained nonconvex optimization},
author = {C. Cartis and N. I. M. Gould and Ph. L. Toint},
journal= {arXiv preprint arXiv:1705.07285},
year = {2021}
}
Comments
32 pages, 3 figures