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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.<\/jats:p>","DOI":"10.1137\/25m1760544","type":"journal-article","created":{"date-parts":[[2026,5,22]],"date-time":"2026-05-22T08:00:51Z","timestamp":1779436851000},"page":"866-886","source":"Crossref","is-referenced-by-count":0,"title":["Duality of Hoffman Constants"],"prefix":"10.1137","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5698-1918","authenticated-orcid":true,"given":"Javier F.","family":"Pe\u00f1a","sequence":"first","affiliation":[{"name":"Carnegie Mellon University, Pittsburgh, Pennsylvia, USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Juan C.","family":"Vera","sequence":"additional","affiliation":[{"name":"Tilburg University, Tilburg, Netherlands."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Luis F.","family":"Zuluaga","sequence":"additional","affiliation":[{"name":"Lehigh University, Bethlehem, Pennsylvania, USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,5,22]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-022-01901-9"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623400375853"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-016-1069-4"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(90)90395-S"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479897316576"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1007\/BF00938589"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1137\/0806015"},{"key":"ref8","unstructured":"J. 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Syst."},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1287\/moor.1100.0456"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(93)90125-8"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-024-02109-9"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1007\/BF02096261"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1137\/0325033"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623401388926"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-92775-6"},{"key":"ref35","unstructured":"B. Natura, Exact Linear Programming Circuits, Curvature, and Diameter, Ph.D. thesis, London School of Economics and Political Science, London, 2022."},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(90)90056-I"},{"key":"ref37","first-page":"1","volume":"44","author":"Pe\u00f1a J.","year":"2019","journal-title":"Math. Oper. Res."},{"key":"ref38","unstructured":"J. Pe\u00f1a, J. Vera, and L. Zuluaga, Equivalence and invariance of the chi and Hoffman constants of a matrix, preprint, https:\/\/arxiv.org\/abs\/1905.06366 (2019)."},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-020-01473-6"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1972-0313769-9"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(73)90007-4"},{"key":"ref42","series-title":"Grundlehren Math. 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