{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T03:58:22Z","timestamp":1759118302854,"version":"3.37.3"},"reference-count":36,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"9","license":[{"start":{"date-parts":[[2015,9,1]],"date-time":"2015-09-01T00:00:00Z","timestamp":1441065600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"}],"funder":[{"DOI":"10.13039\/501100001332","name":"Council for Scientific and Industrial Research Fellowship","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001332","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010892","name":"Department of Science and Technology","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100010892","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001501","name":"University Grants Commission","doi-asserted-by":"publisher","award":["Part (2B) UGC-CAS-(Ph.IV)"],"award-info":[{"award-number":["Part (2B) UGC-CAS-(Ph.IV)"]}],"id":[{"id":"10.13039\/501100001501","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001843","name":"Science and Engineering Research Board","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001843","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001332","name":"Department of Science and Technology","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001332","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Inform. Theory"],"published-print":{"date-parts":[[2015,9]]},"DOI":"10.1109\/tit.2015.2449311","type":"journal-article","created":{"date-parts":[[2015,7,22]],"date-time":"2015-07-22T17:41:13Z","timestamp":1437586873000},"page":"5063-5080","source":"Crossref","is-referenced-by-count":25,"title":["Minimization Problems Based on Relative <inline-formula> <tex-math notation=\"LaTeX\">$\\alpha $ <\/tex-math><\/inline-formula>-Entropy I: Forward Projection"],"prefix":"10.1109","volume":"61","author":[{"given":"M. Ashok","family":"Kumar","sequence":"first","affiliation":[]},{"given":"Rajesh","family":"Sundaresan","sequence":"additional","affiliation":[]}],"member":"263","reference":[{"journal-title":"Lebesgue Integration on Euclidean Space","year":"2001","author":"jones","key":"ref33"},{"journal-title":"Real Analysis Modern Techniques and Their Applications","year":"1999","author":"folland","key":"ref32"},{"key":"ref31","first-page":"329","article-title":"On topological properties of f-divergences","volume":"2","author":"csisz\u00e1r","year":"1967","journal-title":"Stud Sci Math Hungarica"},{"key":"ref30","doi-asserted-by":"crossref","DOI":"10.1007\/978-93-86279-45-3","author":"bhatia","year":"2009","journal-title":"Notes on Functional Analysis"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1109\/18.179378"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1137\/0801014"},{"journal-title":"Real Analysis","year":"1988","author":"royden","key":"ref34"},{"key":"ref10","first-page":"205","article-title":"Information geometry and alternating minimization procedures","author":"csisz\u00e1r","year":"1984","journal-title":"Statist Decisions"},{"key":"ref11","first-page":"637","article-title":"Generalized minimizers of convex integral functionals, Bregman distance, Pythagorean identities","volume":"48","author":"csisz\u00e1r","year":"2012","journal-title":"Kybernetika"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5320-4"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90332-3"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1109\/18.21251"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2006.887466"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1109\/18.481781"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2010.2090221"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2002.1023536"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2014.2329490"},{"key":"ref28","first-page":"299","article-title":"Information-type measures of difference of probability distributions and indirect observations","volume":"2","author":"csisz\u00e1r","year":"1967","journal-title":"Studia Sci Math Hungar"},{"journal-title":"Elements of Information Theory","year":"2006","author":"cover","key":"ref4"},{"article-title":"Minimization problems based on relative $\\alpha$ -entropy II: Reverse projection","year":"2014","author":"ashok kumar","key":"ref27"},{"journal-title":"E T Jaynes Papers on Probability Statistics and Statistical Physics","year":"1982","author":"rosenkrantz","key":"ref3"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176993227"},{"journal-title":"Information and Information Stability of Random Variables and Processes","year":"1964","author":"pinsker","key":"ref29"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1981.1056374"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2003.810633"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176996454"},{"key":"ref2","first-page":"1","article-title":"Relative $\\alpha $ -entropy minimizers subject to linear statistical constraints","author":"ashok kumar","year":"2015","journal-title":"Proc Conf Nat Commun (NCC)"},{"key":"ref9","doi-asserted-by":"crossref","DOI":"10.1561\/9781933019543","volume":"1","author":"csisz\u00e1r","year":"2004","journal-title":"Information Theory and Statistics A Tutorial"},{"key":"ref1","first-page":"1940","article-title":"Further results on geometric properties of a family of relative entropies","author":"ashok kumar","year":"2011","journal-title":"Proc IEEE Int Symp Inf Theory"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1016\/j.anihpb.2006.05.001"},{"key":"ref22","first-page":"211","article-title":"On solutions to multivariate maximum $\\alpha $ -entropy problems","author":"costa","year":"2003","journal-title":"Proc EMMCVPR"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2004.840871"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176348385"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1007\/BF01016429"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2014.2320500"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1109\/18.370121"}],"container-title":["IEEE Transactions on Information Theory"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/18\/7203188\/07132746.pdf?arnumber=7132746","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,1,12]],"date-time":"2022-01-12T16:02:44Z","timestamp":1642003364000},"score":1,"resource":{"primary":{"URL":"http:\/\/ieeexplore.ieee.org\/document\/7132746\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,9]]},"references-count":36,"journal-issue":{"issue":"9"},"URL":"https:\/\/doi.org\/10.1109\/tit.2015.2449311","relation":{},"ISSN":["0018-9448","1557-9654"],"issn-type":[{"type":"print","value":"0018-9448"},{"type":"electronic","value":"1557-9654"}],"subject":[],"published":{"date-parts":[[2015,9]]}}}