Year: 2026
Type: article
Abstract: . We show that a suitable Slater condition implies a duality inequality between the Hoffman constants of the following feasibility problems: [Formula: see text] where [Formula: see text], and [Formula: see text] and [Formula: see text] are reference polyhedral cones, with respective dual cones [Formula: see text] and [Formula: see text]. Our approach relies on an exact characterization of Hoffman constants and introduces a novel Hoffman duality inequality for polyhedral set-valued mappings. These two fundamental results also yield a striking identity between the Hoffman constants of box-constrained feasibility problems, which feature a similar primal-dual structure with a box and a linear subspace as reference sets. Additionally, we establish a surprising identity between the Hoffman constants of box-constrained feasibility problems and the chi condition measures for weighted least-squares problems.
Source: SIAM Journal on Optimization
DOI: 10.1137/25m1760544
Authors: Javier F. Peña, Juan C. Vera, Luis F. Zuluaga
Institutions: Carnegie Mellon University, Tilburg University, Lehigh University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4389912185