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

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 (εg, εH)-second order stationary points in widetildeO(maxεg-3/2, εH-3) iterations. This iteration complexity is achieved for general linearly constrained optimization without cubic regularization of the objective function.