A Riemannian smoothing steepest descent method for non-Lipschitz optimization on submanifolds
(2104.04199)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.
We're not able to analyze this paper right now due to high demand.
Please check back later (sorry!).
Generate a summary of this paper on our Pro plan:
We ran into a problem analyzing this paper.