A TRUST REGION METHOD FOR FINDING SECOND-ORDER STATIONARITY IN LINEARLY CONSTRAINED NONCONVEX OPTIMIZATION

摘要

Motivated by the TRACE algorithm [F. E. Curtis, D. P. Robinson, and M. Samadi, Math. Program., 162 (2017), pp. 1-321, 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 (epsilon(g), epsilon(H))-second-order stationary points in (O) over tilde (max{epsilon(-3/2)(g), epsilon(-3)(H)}) iterations. This iteration complexity is achieved for general linearly constrained optimization without cubic regularization of the objective function.