541. An accelerated projected gradient descent for Grassmannian frame computation
Invited abstract in session WC-6: Structured nonsmooth optimization -- Part III, stream Nonsmooth and nonconvex optimization.
Wednesday, 14:00-16:00Room: B100/7013
Authors (first author is the speaker)
| 1. | Bastien Massion
|
| ICTEAM (INMA), UCLouvain | |
| 2. | Estelle Massart
|
Abstract
This paper addresses the approximation of real and complex Grassmannian frames, namely sets of unit-norm vectors with minimum mutual coherence. We recast this problem as a collection of feasibility problems aiming to design frames with given target coherence, that evolves during the execution of the algorithm. The feasibility problems are solved by an accelerated alternating projection algorithm inspired by accelerated proximal methods, leveraging a Gram matrix representation of the frames. Numerical experiments indicate that our proposed Targeted coherence with Accelerated Alternating Projection (TAAP) algorithm outperforms state-of-the-art methods regarding the mutual coherence vs computational cost criterion, exhibiting the largest performance gap with existing methods when the frame dimension is comparable to the dimension of the ambient space.
Keywords
- Optimization for learning and data analysis
- Multi-level optimization
- Linear and nonlinear optimization
Status: accepted
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