187. A Unified Constrained Saddle Dynamics for Index-1 Saddle Point Search on Riemannian Submanifolds
Invited abstract in session TB-11: Advances in Manifold Optimization, stream Riemannian Manifold and Conic Optimization.
Tuesday, 10:30-12:30Room: B100/5017
Authors (first author is the speaker)
| 1. | Yukuan Hu
|
| CERMICS, École nationale des ponts et chaussées, Institut Polytechnique de Paris |
Abstract
Index-1 saddle point search on Riemannian submanifolds is a fundamental task in various applications. However, most existing works concentrate on unconstrained settings, with only limited efforts devoted to the cases with special Riemannian submanifolds induced by global defining functions. In this talk, we introduce a unified constrained saddle dynamics applicable to general Riemannian submanifolds, where the position and direction variables are simultaneously evolved on the tangent bundle. In particular, the direction dynamics leverages the second fundamental form to maintain feasibility. The linear stability of the dynamics at index-1 saddle points is established. We further discretize the proposed dynamics using the Riemannian manifold tools. The local convergence properties of the resulting iterative methods are analyzed. Finally, the numerical experiments on electronic excited states calculations demonstrate the effectiveness of the proposed methods.
Keywords
- First-order optimization
- Computational mathematical optimization
- Applications of continuous optimization
Status: accepted
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