{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T07:58:54Z","timestamp":1787385534338,"version":"build-2736575974"},"reference-count":14,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>In their recent paper from 2009 [SIAM J. Control Optim., 48 (2009), pp. 787\u2013811], J. Eckstein and B. F. Svaiter proposed a very general and flexible splitting framework for finding a zero of the sum of finitely many maximal monotone operators. In this short note, we provide a technical result that allows for the removal of Eckstein and Svaiter's assumption that the sum of the operators be maximal monotone or that the underlying Hilbert space be finite-dimensional.<\/jats:p>","DOI":"10.1137\/090759690","type":"journal-article","created":{"date-parts":[[2009,8,17]],"date-time":"2009-08-17T11:23:29Z","timestamp":1250508209000},"page":"2513-2515","source":"Crossref","is-referenced-by-count":19,"title":["A Note on the Paper by Eckstein and Svaiter on \u201cGeneral Projective Splitting Methods for Sums of Maximal Monotone Operators\u201d"],"prefix":"10.1137","volume":"48","author":[{"given":"Heinz H.","family":"Bauschke","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,8,14]]},"reference":[{"key":"R1","unstructured":"R.S. Burachik and A.N. Iusem,\n                      Set-Valued Mappings and Enlargements of Monotone Operators\n                      , Springer-Verlag, Berlin, 2008."},{"key":"R2","unstructured":"P.L. Combettes,\n                      Iterative construction of the resolvent of a sum of maximal monotone operators\n                      , J. Convex Anal., 16 (2009)."},{"key":"R3","unstructured":"J.B. Conway,\n                      A Course in Functional Analysis\n                      , 2nd ed., Springer-Verlag, Berlin, 1990."},{"key":"R4","unstructured":"J. Eckstein,\n                      Splitting methods for monotone operators with applications to parallel optimization\n                      , Ph.D. thesis, Department of Civil Engineering, Massachusetts Institute of Technology, Boston, 1989."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01581204"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1287\/ijoc.10.2.218"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/070698816"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"K. Goebel and W.A. Kirk,\n                      Topics in Metric Fixed Point Theory\n                      , Cambridge University Press, London, 1990.","DOI":"10.1017\/CBO9780511526152"},{"key":"R9","unstructured":"K. Goebel and S. Reich,\n                      Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings\n                      , Marcel Dekker, New York, 1984."},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-55.3.605"},{"key":"R11","unstructured":"R.T. Rockafellar and R.J-B Wets,\n                      Variational Analysis\n                      , 2nd printing, Springer-Verlag, Berlin, 2004."},{"key":"R12","doi-asserted-by":"crossref","unstructured":"S. Simons,\n                      Minimax and Monotonicity\n                      , Springer-Verlag, Berlin, 1998.","DOI":"10.1007\/BFb0093633"},{"key":"R13","unstructured":"S. Simons,\n                      From Hahn-Banach to Monotonicity\n                      , Springer-Verlag, Berlin, 2008."},{"key":"R14","doi-asserted-by":"crossref","unstructured":"C. Z\u0103linescu,\n                      Convex Analysis in General Vector Spaces\n                      , World Scientific Publishing, River Edge, NJ, 2002.","DOI":"10.1142\/5021"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/090759690","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:52:01Z","timestamp":1787316721000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/090759690"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1]]},"references-count":14,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2009,1]]}},"alternative-id":["10.1137\/090759690"],"URL":"https:\/\/doi.org\/10.1137\/090759690","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1]]}}}