A Riemannian smoothing steepest descent method for non-Lipschitz optimization on submanifolds
Abstract
In this paper, we propose a Riemannian smoothing steepest descent method to minimize a nonconvex and non-Lipschitz function on submanifolds. The generalized subdifferentials on Riemannian manifold and the Riemannian gradient sub-consistency are defined and discussed. We prove that any accumulation point of the sequence generated by the Riemannian smoothing steepest descent method is a stationary point associated with the smoothing function employed in the method, which is necessary for the local optimality of the original non-Lipschitz problem. Under the Riemannian gradient sub-consistency condition, we also prove that any accumulation point is a Riemannian limiting stationary point of the original non-Lipschitz problem. Numerical experiments are conducted to demonstrate the efficiency of the proposed method.
Cite
@article{arxiv.2104.04199,
title = {A Riemannian smoothing steepest descent method for non-Lipschitz optimization on submanifolds},
author = {Chao Zhang and Xiaojun Chen and Shiqian Ma},
journal= {arXiv preprint arXiv:2104.04199},
year = {2021}
}