136. A space-decoupling framework for optimization on bounded-rank matrices with orthogonally invariant constraints
Invited abstract in session WC-49: Aspects of Conic Optimization, stream Conic and polynomial optimization.
Wednesday, 12:30-14:00Room: Parkinson B10
Authors (first author is the speaker)
| 1. | Bin Gao
|
| Chinese Academy of Sciences |
Abstract
Imposing additional constraints on low-rank optimization has garnered growing interest. However, the geometry of coupled constraints hampers the well-developed low-rank structure and makes the problem nonsmooth and intricate. To this end, we propose a space-decoupling framework for optimization on bounded-rank matrices with orthogonally invariant constraints. The "space-decoupling" is reflected in several ways. We show that the tangent cone of coupled constraints is the intersection of tangent cones of each constraint. Moreover, we decouple the intertwined bounded-rank and orthogonally invariant constraints into two spaces, leading to optimization on a smooth manifold. Implementing Riemannian algorithms on this manifold is painless as long as the geometry of additional constraints is known. In addition, we unveil the equivalence between the original problem and the reformulated problem. Numerical experiments on real-world applications---spherical data fitting, graph similarity measuring, model reduction of Markov processes, reinforcement learning, low-rank SDP, and deep learning---validate the superiority of the proposed framework.
Keywords
- Continuous Optimization
- Programming, Nonlinear
- Mathematical Programming
Status: accepted
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