GPU-friendly and Linearly Convergent First-order Methods for Certifying Optimal $k$-sparse GLMs
We investigate the problem of certifying optimality for sparse generalized linear models (GLMs), where sparsity is enforced through a cardinality constraint. While Branch-and-Bound (BnB) frameworks can certify optimality using perspective relaxations, existing methods for solving these relaxations are computationally intensive, limiting their scalability. To address this challenge, we reformulate the relaxations as composite optimization problems and develop a unified proximal framework that is both linearly convergent and computationally efficient. Under specific geometric regularity conditions, our analysis links primal quadratic growth to dual quadratic decay, yielding error bounds tha...
| Authors | Jiachang Liu, Andrea Lodi, Soroosh Shafiee |
|---|---|
| Primary category | math.OC |
| Published | 1 March 2026 |
| Last updated at source | 1 March 2026 |
Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 17 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.