395. Critical Point Theory for Sparse Huber Recovery
Invited abstract in session MD-13: Recent advances in optimization problems with cardinality constraints, stream Sparsity guarantee and cardinality-constrained (MI)NLPs.
Monday, 16:30-18:30Room: B100/6009
Authors (first author is the speaker)
| 1. | Deniz Akkaya
|
| Bilkent University | |
| 2. | Mustafa Pinar
|
| Department of Industrial Engineering, Bilkent University |
Abstract
We study the problem of sparse recovery in compressed sensing, aiming to minimize sensing error in linear measurements using sparse vectors with a fixed number of nonzero entries. To improve robustness against outliers, we employ the Huber loss, which effectively reduces the influence of Gaussian noise while preserving sensitivity to small deviations. Extending classical results from the sum of squared errors to the non-smooth setting of Huber loss presents nontrivial challenges, which we address in this work.
Our analysis is grounded in critical point theory, where we establish key properties such as non-degeneracy, genericity, and stability. Furthermore, we extend Morse theory to the Huber loss framework and conduct a detailed examination of saddle points. These results offer deeper insights into the theoretical landscape of sparse recovery, shedding light on its structural complexity and optimization challenges.
Keywords
- Linear and nonlinear optimization
- Non-smooth optimization
- Global optimization
Status: accepted
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