A trust region method for finding second-order stationarity in linearly constrained nonconvex optimization

Abstract

Motivated by the TRACE algorithm [F. E. Curtis, D. P. Robinson, and M. Samadi, Math. Program., 162 (2017), pp. 1-32], we propose a trust region algorithm for finding second-order stationary points of a linearly constrained nonconvex optimization problem. We show the convergence of the proposed algorithm to (ϵ g, ϵ H)-second-order stationary points in O(max{ϵ -3/2 g, ϵ -3 H}) iterations. This iteration complexity is achieved for general linearly constrained optimization without cubic regularization of the objective function. © 2020 Society for Industrial and Applied Mathematics.