{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T08:00:24Z","timestamp":1787385624602,"version":"build-2736575974"},"reference-count":11,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1514559"],"award-info":[{"award-number":["DMS-1514559"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>Generalized matrix-fractional (GMF) functions are a class of matrix support functions introduced by Burke and Hoheisel as a tool for unifying a range of seemingly divergent matrix optimization problems associated with inverse problems, regularization, and learning. In this paper we dramatically simplify the support function representation for GMF functions as well as the representation of their subdifferentials. These new representations allow the ready computation of a range of important related geometric objects whose formulations were previously unavailable.<\/jats:p>","DOI":"10.1137\/17m1119524","type":"journal-article","created":{"date-parts":[[2018,8,2]],"date-time":"2018-08-02T13:02:02Z","timestamp":1533214922000},"page":"2189-2200","source":"Crossref","is-referenced-by-count":4,"title":["Convex Geometry of the Generalized Matrix-Fractional Function"],"prefix":"10.1137","volume":"28","author":[{"given":"James V.","family":"Burke","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuan","family":"Gao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tim","family":"Hoheisel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,8,2]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"H. H. Bauschke and P. L. Combettes,\n                      Convex Analysis and Monotone Operator Theory in Hilbert Spaces\n                      , CMS Books Math., Springer, New York, 2011.","DOI":"10.1007\/978-1-4419-9467-7"},{"key":"atypb2","doi-asserted-by":"crossref","unstructured":"S. Boyd and L. Vandenbergh,\n                      Convex Optimization\n                      , Cambridge University Press, Cambridge, 2004.","DOI":"10.1017\/CBO9780511804441"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/140984178"},{"key":"atypb4","unstructured":"J. Dattorro,\n                      Convex Optimization & Euclidean Distance Geometry\n                      , v. 2014.04.08, Meboo Publishing USA, Palo Alto, CA, 2005; available athttp:\/\/www.convexoptimization.com\/TOOLS\/0976401304_v2014.04.08.pdf."},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/BF02591851"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/15M1034283"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1137\/130940785"},{"key":"atypb8","doi-asserted-by":"crossref","unstructured":"J. Gallier,\n                      Geometric Methods and Applications: For Computer Science and Engineering\n                      , Texts Appl. Math. 38, Springer, New York, 2011.","DOI":"10.1007\/978-1-4419-9961-0"},{"key":"atypb9","first-page":"575","volume":"32","author":"Hsieh C.-J.","year":"2014","journal-title":"Proc. Mach. Learn. Res."},{"key":"atypb10","unstructured":"R. T. Rockafellar,\n                      Convex Analysis\n                      , Princeton University Press, Princeton, NJ, 1970."},{"key":"atypb11","doi-asserted-by":"crossref","unstructured":"R. T. Rockafellar and R. J.B. Wets,\n                      Variational Analysis\n                      , Grundlehren Math. Wiss. 317, Springer, Berlin, 1998.","DOI":"10.1007\/978-3-642-02431-3"}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/17M1119524","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:18:58Z","timestamp":1787339938000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/17M1119524"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":11,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1137\/17M1119524"],"URL":"https:\/\/doi.org\/10.1137\/17m1119524","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]}}}