A Riemannian smoothing steepest descent method for non-Lipschitz optimization on submanifolds

Chao Zhang; Xiaojun Chen; Shiqian Ma

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arXiv · 2104.04199

A Riemannian smoothing steepest descent method for non-Lipschitz optimization on submanifolds

Chao Zhang·Xiaojun Chen·Shiqian Ma

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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.

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BibTeX RIS

Chao Zhang, Xiaojun Chen, Shiqian Ma. 2021-04-09. A Riemannian smoothing steepest descent method for non-Lipschitz optimization on submanifolds. https://arxiv.org/abs/2104.04199

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