{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:26:48Z","timestamp":1787318808471,"version":"build-2736575974"},"reference-count":49,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces, and its convergence is established under the assumption that solutions exist. Unlike existing alternating algorithms, which are limited to two variables and linear coupling, our parallel method can handle an arbitrary number of variables as well as nonlinear coupling schemes. The breadth and flexibility of the proposed framework is illustrated through applications in the areas of evolution inclusions, variational problems, best approximation, and network flows.<\/jats:p>","DOI":"10.1137\/090754297","type":"journal-article","created":{"date-parts":[[2010,1,22]],"date-time":"2010-01-22T18:11:24Z","timestamp":1264183884000},"page":"3246-3270","source":"Crossref","is-referenced-by-count":81,"title":["A Parallel Splitting Method for Coupled Monotone Inclusions"],"prefix":"10.1137","volume":"48","author":[{"given":"H\u00e9dy","family":"Attouch","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Luis M.","family":"Brice\u00f1o-Arias","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Patrick L.","family":"Combettes","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,1,22]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.5802\/afst.541"},{"key":"R2","unstructured":"H. Attouch,\n                      Variational Convergence for Functions and Operators,\n                      Pitman, Boston, MA, 1984."},{"key":"R3","first-page":"485","volume":"15","author":"Attouch H.","year":"2008","journal-title":"J. Convex Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0944-6532","issn-type":"print"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/060657248"},{"key":"R5","unstructured":"J.P. Aubin and H. Frankowska,\n                      Set-Valued Analysis,\n                      Birkh\u00e4user, Boston, MA, 1990."},{"key":"R6","unstructured":"A. Auslender,\n                      Probl\u00e8mes de minimax via l'analyse convexe et les in\u00e9galit\u00e9s variationnelles: Th\u00e9orie et algorithmes,\n                      Lecture Notes in Econom. and Math. Systems 77, Springer-Verlag, New York, 1972."},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1007\/BF03007664"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1007\/BF01027691"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1006\/jath.1994.1136"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144593251710"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jat.2004.02.006"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2004.07.054"},{"key":"R13","unstructured":"M. Beckmann, C. McGuire, and C. Winsten,\n                      Studies in Economics of Transportation,\n                      Yale University Press, New Haven, CT, 1956."},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0120965"},{"key":"R15","unstructured":"H. Br\u00e9zis,\n                      Op\u00e9rateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert,\n                      North-Holland\/Elsevier, New York, 1973."},{"key":"R16","doi-asserted-by":"crossref","unstructured":"H. Br\u00e9zis and M. Sibony,\n                      M\u00e9thodes d'approximation et d'it\u00e9ration pour les op\u00e9rateurs monotones,\n                      Arch. Ration. Mech. Anal., 28 (1967\/1968), pp. 59\u201382.","DOI":"10.1007\/BF00281564"},{"key":"R17","unstructured":"Y. Censor and S. A. Zenios,\n                      Parallel Optimization: Theory, Algorithms, and Applications,\n                      Oxford University Press, New York, 1997."},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1959-0105008-8"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1109\/5.214546"},{"key":"R20","first-page":"1385","volume":"320","author":"Combettes P. L.","year":"1995","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. I Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0764-4442","issn-type":"print"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1007\/BF02683333"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1080\/02331930412331327157"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1109\/78.782189"},{"key":"R24","first-page":"633","volume":"13","author":"Combettes P. L.","year":"2006","journal-title":"J. Convex Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0944-6532","issn-type":"print"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012903427336"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1137\/050626090"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(76)90152-9"},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1985.1085777"},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1016\/0041-5553(67)90113-9"},{"key":"R30","doi-asserted-by":"crossref","unstructured":"A. Haraux,\n                      Nonlinear evolution equations: Global behavior of solutions,\n                      Lecture Notes in Math. 841, Springer-Verlag, New York, 1981.","DOI":"10.1007\/BFb0089606"},{"key":"R31","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-002-0408-y"},{"key":"R32","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012998333116"},{"key":"R33","first-page":"29","volume":"6","author":"Lehdili N.","year":"1999","journal-title":"Comm. Appl. Nonlinear Anal."},{"key":"R34","doi-asserted-by":"publisher","DOI":"10.1016\/0041-5553(66)90114-5"},{"key":"R35","doi-asserted-by":"crossref","unstructured":"B. Mercier,\n                      Topics in finite element solution of elliptic problems,\n                      Lectures on Mathematics 63, Tata Institute of Fundamental Research, Bombay, 1979.","DOI":"10.1007\/978-3-662-00973-4"},{"key":"R36","doi-asserted-by":"publisher","DOI":"10.24033\/bsmf.1625"},{"key":"R37","unstructured":"M. Patriksson,\n                      The Traffic Assignment Problem: Models and Methods,\n                      V.S.P. Int'l Science, Utrecht, The Netherlands, 1994."},{"key":"R38","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(66)90027-8"},{"key":"R39","unstructured":"B. T. Polyak,\n                      Introduction to Optimization,\n                      Optimization Software Inc., New York, 1987."},{"key":"R40","unstructured":"R. T. Rockafellar,\n                      Network Flows and Monotropic Optimization\n                      , Wiley, New York, 1984."},{"key":"R41","unstructured":"Y. Sheffi,\n                      Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods,\n                      Prentice-Hall, Englewood Cliffs, NJ, 1985."},{"key":"R42","unstructured":"R. E. Showalter,\n                      Monotone operators in Banach space and nonlinear partial differential equations\n                      , Mathematical Surveys and Monographs 49, American Mathematical Society, Providence, RI, 1997."},{"key":"R43","doi-asserted-by":"publisher","DOI":"10.1007\/BF02575559"},{"key":"R44","unstructured":"S. Simons,\n                      From Hahn-Banach to monotonicity,\n                      Lecture Notes in Math. 1693, Springer-Verlag, New York, 2008."},{"key":"R45","doi-asserted-by":"publisher","DOI":"10.1680\/ipeds.1952.11259"},{"key":"R46","doi-asserted-by":"crossref","unstructured":"C. Z\u0103linescu,\n                      Convex Analysis in General Vector Spaces,\n                      World Scientific, River Edge, NJ, 2002.","DOI":"10.1142\/5021"},{"key":"R47","unstructured":"E. Zeidler,\n                      Nonlinear Functional Analysis and Its Applications\n                      I, Springer-Verlag, New York, 1993."},{"key":"R48","doi-asserted-by":"crossref","unstructured":"E. Zeidler,\n                      Nonlinear Functional Analysis and Its Applications\n                      II, Springer-Verlag, New York, 1990.","DOI":"10.1007\/978-1-4612-0985-0"},{"key":"R49","first-page":"714","volume":"6","author":"Zhu D. L.","year":"1996","journal-title":"J. Optim.","ISSN":"https:\/\/id.crossref.org\/issn\/0150-536X","issn-type":"print"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/090754297","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:40:49Z","timestamp":1787316049000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/090754297"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":49,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/090754297"],"URL":"https:\/\/doi.org\/10.1137\/090754297","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}