Explicit Bounds on Hoffman Constants for Sparse Polyhedral Regularizers
Hoffman constants quantify the distance to the solution set of a polyhedral system in terms of its residual; they control error bounds, geometric conditioning, the convergence rate of first-order iterative algorithms, and the stability of regression estimators to target perturbations. Despite their importance, explicit values of Hoffman constants are rarely available due to their computational complexity. In this paper, we derive explicit bounds on the Hoffman constant for a class of structured polyhedral systems arising in sparse regularization. We show that the constants admit a decomposition into spectral, geometric, and interaction components, which together determine their scaling be...
| Authors | Faris Chaudhry, Anthea Monod, Keisuke Yano |
|---|---|
| Primary category | math.OC |
| Published | 11 October 2026 |
| Last updated at source | 11 October 2026 |
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