Primal-Dual Methods for Nonsmooth Nonconvex Optimization with Orthogonality Constraints
Recent advancements in data science have significantly elevated the importance of orthogonally constrained optimization problems. The Riemannian approach has become a popular technique for addressing these problems due to the advantageous computational and analytical properties of the Stiefel manifold. Nonetheless, the interplay of nonsmoothness alongside orthogonality constraints introduces substantial challenges to current Riemannian methods, including scalability, parallelizability, complicated subproblems, and cumulative numerical errors that threaten feasibility. In this paper, we take a retraction-free primal-dual approach and propose a linearized smoothing augmented Lagrangian meth...
| Authors | Linglingzhi Zhu, Wentao Ding, Shangyuan Liu et al. |
|---|---|
| Primary category | math.OC |
| Published | 5 April 2026 |
| Last updated at source | 5 April 2026 |
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