{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,10]],"date-time":"2026-08-10T07:29:44Z","timestamp":1786346984848,"version":"build-2736575974"},"reference-count":29,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"name":"MATH-AMSUD 23-MATH-09","award":["AMSUD230018"],"award-info":[{"award-number":["AMSUD230018"]}]},{"DOI":"10.13039\/100031750","name":"Universidad de O\u2019Higgins","doi-asserted-by":"crossref","award":["MOVI2430"],"award-info":[{"award-number":["MOVI2430"]}],"id":[{"id":"10.13039\/100031750","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100031750","name":"Universidad de O\u2019Higgins","doi-asserted-by":"crossref","award":["PNTE2502"],"award-info":[{"award-number":["PNTE2502"]}],"id":[{"id":"10.13039\/100031750","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[2026,9,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>This work introduces a novel dissimilarity measure between two convex cones, based on the max-min angle between them. We demonstrate that this measure is closely related to the Pompeiu\u2013Hausdorff distance, a well-established metric for comparing compact sets. Furthermore, we examine cone configurations where the measure admits simplified or analytic forms. For the specific case of polyhedral cones, a nonconvex cutting-plane method is deployed to compute, at least approximately, the measure between them. Our approach builds on a tailored version of Kelley\u2019s cutting-plane algorithm, which involves solving a challenging master program per iteration. When this master program is solved locally, our method yields an angle that satisfies certain necessary optimality conditions of the underlying nonconvex optimization problem yielding the dissimilarity measure between the cones. As an application of the proposed mathematical and algorithmic framework, we address the image-set classification task under limited data conditions, a task that falls within the scope of the few-shot learning paradigm. In this context, image sets belonging to the same class are modeled as polyhedral cones, and our dissimilarity measure proves useful for understanding whether two image sets belong to the same class.<\/jats:p>","DOI":"10.1137\/25m1794371","type":"journal-article","created":{"date-parts":[[2026,8,10]],"date-time":"2026-08-10T07:00:41Z","timestamp":1786345241000},"page":"1706-1730","source":"Crossref","is-referenced-by-count":0,"title":["Measuring Dissimilarity between Convex Cones by Means of Max-Min Angles"],"prefix":"10.1137","volume":"36","author":[{"given":"Welington","family":"de Oliveira","sequence":"first","affiliation":[{"name":"Mines Paris, Universit\u00e9 PSL, Centre de Math\u00e9matiques Appliqu\u00e9es (CMA), Sophia Antipolis, F-06904, France."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0083-2515","authenticated-orcid":true,"given":"Valentina","family":"Sessa","sequence":"additional","affiliation":[{"name":"Mines Paris, Universit\u00e9 PSL, Centre de Math\u00e9matiques Appliqu\u00e9es (CMA), Sophia Antipolis, F-06904, France."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3344-1067","authenticated-orcid":true,"given":"David","family":"Sossa","sequence":"additional","affiliation":[{"name":"Universidad de O\u2019Higgins, Instituto de Ciencias de la Ingenier\u00eda, Av. Libertador Bernardo O\u2019Higgins 611, Rancagua, Chile."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,8,10]]},"reference":[{"key":"ref1","volume-title":"Internat. Ser. Oper. Res. Management Sci. 363","author":"van Ackooij W. 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