2024年07月18日 星期四 登录 EN

学术活动
A Constraint Dissolving Approach for Nonsmooth Optimization over the Stiefel Manifold
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报告人:
Nachuan Xiao, Doctor, National University of Singapore
邀请人:
Yaxiang Yuan, Professor
题目:
A Constraint Dissolving Approach for Nonsmooth Optimization over the Stiefel Manifold
时间地点:
15:30-16:30 December 21 (Thursday), Z311
摘要:

This talk focuses on the minimization of a possibly nonsmooth objective function over the Stiefel manifold. The existing approaches either lack efficiency or can only tackle prox-friendly objective functions.  We propose a constraint dissolving function named NCDF and show that it has the same first-order stationary points and local minimizers as the original problem in a neighborhood of the Stiefel manifold. Furthermore, we show that the Clarke subdifferential of NCDF is easy to achieve from the Clarke subdifferential of the objective function. Therefore, various existing approaches for unconstrained nonsmooth optimization can be directly applied to nonsmooth optimization problems over the Stiefel manifold. We propose a framework for developing subgradient-based methods and establishing their convergence properties based on prior works. Furthermore, based on our proposed framework, we can develop efficient approaches for optimization over the Stiefel manifold. Preliminary numerical experiments further highlight that the proposed constraint dissolving approach yields efficient and direct implementations of various unconstrained approaches to nonsmooth optimization problems over the Stiefel manifold.