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arXiv · 1904.06784

A Trust Region Method for Finding Second-Order Stationarity in Linearly Constrained Non-Convex Optimization

Maher Nouiehed·Meisam Razaviyayn
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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.

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Maher Nouiehed, Meisam Razaviyayn. 2019-04-14. A Trust Region Method for Finding Second-Order Stationarity in Linearly Constrained Non-Convex Optimization. https://arxiv.org/abs/1904.06784

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