A Trust Region Method for Finding Second-Order Stationarity in Linearly Constrained Non-Convex Optimization
Optimization and Control
2019-04-16 v1
Abstract
Motivated by TRACE algorithm [Curtis et al. 2017], we propose a trust region algorithm for finding second order stationary points of a linearly constrained non-convex optimization problem. We show the convergence of the proposed algorithm to (\epsilon_g, \epsilon_H)-second order stationary points in \widetilde{\mathcal{O}}(\max{\epsilon_g^{-3/2}, \epsilon_H^{-3}}) iterations. This iteration complexity is achieved for general linearly constrained optimization without cubic regularization of the objective function.
Cite
@article{arxiv.1904.06784,
title = {A Trust Region Method for Finding Second-Order Stationarity in Linearly Constrained Non-Convex Optimization},
author = {Maher Nouiehed and Meisam Razaviyayn},
journal= {arXiv preprint arXiv:1904.06784},
year = {2019}
}