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Biomed. Eng."},{"key":"ref2","first-page":"539","volume":"284","author":"Attouch H.","year":"1977","journal-title":"C.R. Acad. Sci. Paris"},{"key":"ref3","volume-title":"Variational Convergence for Functions and Operators","author":"Attouch H.","year":"1984"},{"key":"ref4","volume-title":"Asymptotic Cones and Functions in Optimization and Variational Inequalities","author":"Auslender A.","year":"2003"},{"key":"ref5","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-48311-5_31","volume-title":"Convex Analysis and Monotone Operator Theory in Hilbert Spaces.","author":"Bauschke H.","year":"2019"},{"key":"ref6","volume-title":"Probability and Measure","author":"Billingsley P.","year":"2017"},{"key":"ref7","volume-title":"Fundamentals of Statistical Exponential Families: With Applications in Statistical Decision Theory","author":"Brown L. D.","year":"1986"},{"key":"ref8","author":"Burke J.","year":"2015","journal-title":"Optimization Online"},{"key":"ref9","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1007\/BF01582063","volume":"63","author":"Byrd R. H.","year":"1994","journal-title":"Math. Program."},{"key":"ref10","doi-asserted-by":"crossref","first-page":"2316","DOI":"10.1038\/s41598-022-06082-1","volume":"12","author":"Cai Z.","year":"2022","journal-title":"Sci. Rep."},{"key":"ref11","doi-asserted-by":"crossref","first-page":"E55969","DOI":"10.1371\/journal.pone.0055969","volume":"8","author":"Chowdhury R. A.","year":"2013","journal-title":"PLoS One"},{"key":"ref12","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1016\/0047-259X(83)90037-4","volume":"13","author":"Cs\u00f6rg\u0151 S.","year":"1983","journal-title":"J. Multivariate Anal."},{"key":"ref13","first-page":"139","volume-title":"Colloquia Mathematica Societatis J\u00e1nos Bolyai 32, Nonparametric Statistical Inference","author":"Cs\u00f6rg\u0151 S.","year":"1980"},{"key":"ref14","first-page":"567","volume":"26","author":"Dacunha-Castelle D.","year":"1990","journal-title":"Ann. Inst. Henri Poincar\u00e9 Probab. Stat."},{"key":"ref15","doi-asserted-by":"crossref","first-page":"725","DOI":"10.1016\/j.ejmp.2014.05.002","volume":"30","author":"den Dekker A.","year":"2014","journal-title":"Phys. Med."},{"key":"ref16","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1109\/MSP.2012.2211477","volume":"29","author":"Deng L.","year":"2012","journal-title":"IEEE Signal Process. Mag."},{"key":"ref17","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1002\/cpa.3160290405","volume":"29","author":"Donsker M. D.","year":"1976","journal-title":"Comm. Pure. Appl. Math."},{"key":"ref18","first-page":"1","volume":"4","author":"Fermin A.","year":"2006","journal-title":"Int. J. Tomogr. Stat."},{"key":"ref19","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1093\/biomet\/76.3.457","volume":"76","author":"Feuerverger A.","year":"1989","journal-title":"Biometrika"},{"key":"ref20","volume-title":"Real Analysis: Modern Techniques and Their Applications","volume":"40","author":"Folland G.","year":"1999"},{"key":"ref21","unstructured":"F. Gamboa, M\u00e9thode du maximum d\u2019entropie sur la moyenne et applications, Ph.D. thesis, Universit\u00e9 Paris-Sud, 1989."},{"key":"ref22","doi-asserted-by":"crossref","first-page":"734","DOI":"10.1016\/j.neuroimage.2005.08.053","volume":"29","author":"Grova C.","year":"2006","journal-title":"Neuroimage"},{"key":"ref23","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1007\/s10548-014-0423-1","volume":"29","author":"Heers M.","year":"2016","journal-title":"Brain Topogr."},{"key":"ref24","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1103\/PhysRev.106.620","volume":"106","author":"Jaynes E. T.","year":"1957","journal-title":"Phys. Rev."},{"key":"ref25","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1103\/PhysRev.108.171","volume":"108","author":"Jaynes E. T.","year":"1957","journal-title":"II, Phys. Rev."},{"key":"ref26","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1214\/14-STS511","volume":"30","author":"Kantas N.","year":"2015","journal-title":"Statist. Sci."},{"key":"ref27","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1080\/17442509108833676","volume":"34","author":"King A. J.","year":"1991","journal-title":"Stoch. Stoch. Rep."},{"key":"ref28","volume-title":"Probability Theory: A Comprehensive Course","author":"Klenke A.","year":"2013"},{"key":"ref29","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1214\/aoms\/1177729694","volume":"22","author":"Kullback S.","year":"1951","journal-title":"Ann. Math. Stat."},{"key":"ref30","doi-asserted-by":"crossref","first-page":"1565","DOI":"10.1109\/18.771159","volume":"45","author":"Le Besnerais G.","year":"1999","journal-title":"IEEE Trans. Inform. Theory"},{"key":"ref31","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1088\/0266-5611\/13\/1\/011","volume":"13","author":"Mar\u00e9chal P.","year":"1997","journal-title":"Inverse Problems"},{"key":"ref32","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1107\/S0108767385000526","volume":"41","author":"Navaza J.","year":"1985","journal-title":"Acta Crystallogr. Sect.\u00a0A"},{"key":"ref33","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1107\/S0108767386099397","volume":"42","author":"Navaza J.","year":"1986","journal-title":"Acta Crystallogr. Sect.\u00a0A"},{"key":"ref34","first-page":"489","volume":"42","author":"Rietsch E.","year":"1976","journal-title":"J. Geophys."},{"key":"ref35","doi-asserted-by":"crossref","first-page":"015011","DOI":"10.1088\/1361-6420\/abc32e","volume":"37","author":"Rioux G.","year":"2020","journal-title":"Inverse Problems"},{"key":"ref36","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1109\/TPAMI.2019.2927311","volume":"43","author":"Rioux G.","year":"2021","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref37","volume-title":"Convex Analysis","author":"Rockafellar R. T.","year":"1997"},{"key":"ref38","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-02431-3","volume-title":"Variational Analysis","author":"Rockafellar R. T.","year":"1998"},{"key":"ref39","unstructured":"R. T. Rockafellar and R. Wets, Variational systems, an introduction, in Multifunctions and Integrands: Stochastic Analysis, Approximation and Optimization,\u00a0Proceedings of a Conference Held in Catania, Italy, June 1983, Springer-Verlag, Berlin,\u00a02006, pp. 1\u201354."},{"key":"ref40","doi-asserted-by":"crossref","first-page":"961","DOI":"10.1137\/060657716","volume":"18","author":"R\u00f6misch W.","year":"2007","journal-title":"SIAM J. Optim."},{"key":"ref41","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-030-76275-9","volume-title":"An Optimization Primer","author":"Royset J.","year":"2021"},{"key":"ref42","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511610547","volume-title":"Elements of Distribution Theory","author":"Severini T.","year":"2005"},{"key":"ref43","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1088\/0954-898X_14_3_302","volume":"14","author":"Torralba A.","year":"2003","journal-title":"Netw. Comput. Neural Syst."},{"key":"ref44","doi-asserted-by":"crossref","first-page":"779","DOI":"10.1088\/0266-5611\/12\/5\/017","volume":"12","author":"Urban B.","year":"1996","journal-title":"Inverse Problems"},{"key":"ref45","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1007\/s10107-024-02189-7","volume":"214","author":"Vaisbourd Y.","year":"2025","journal-title":"Math. Program."},{"key":"ref46","doi-asserted-by":"crossref","first-page":"2128","DOI":"10.1214\/aop\/1041903221","volume":"24","author":"van der Vaart A.","year":"1996","journal-title":"Ann. Probab."},{"key":"ref47","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2545-2","volume-title":"Weak Convergence and Empirical Processes: With Applications to Statistics","author":"van der Vaart A.","year":"1996"},{"key":"ref48","unstructured":"H. Xiao, K. Rasul, and R. Vollgraf, Fashion-MNIST: A Novel Image Dataset for Benchmarking Machine Learning Algorithms, preprint, https:\/\/arxiv.org\/abs\/1708.07747, 2017."},{"key":"ref49","doi-asserted-by":"crossref","DOI":"10.1142\/5021","volume-title":"Convex Analysis in General Vector Spaces","author":"Z\u01celinescu C.","year":"2002"}],"container-title":["SIAM Journal on Mathematics of Data Science"],"original-title":[],"language":"en","deposited":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T08:25:25Z","timestamp":1770884725000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/24M1720494"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,12]]},"references-count":49,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,3,31]]}},"alternative-id":["10.1137\/24M1720494"],"URL":"https:\/\/doi.org\/10.1137\/24m1720494","relation":{},"ISSN":["2577-0187"],"issn-type":[{"value":"2577-0187","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,12]]}}}