{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:20:50Z","timestamp":1740122450478,"version":"3.37.3"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2018,12,15]],"date-time":"2018-12-15T00:00:00Z","timestamp":1544832000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100004396","name":"Thailand Research Fund","doi-asserted-by":"publisher","award":["RSA5880028"],"award-info":[{"award-number":["RSA5880028"]}],"id":[{"id":"10.13039\/501100004396","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2019,4]]},"DOI":"10.1007\/s10898-018-00730-5","type":"journal-article","created":{"date-parts":[[2019,3,7]],"date-time":"2019-03-07T12:47:04Z","timestamp":1551962824000},"page":"825-847","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Generalized forward\u2013backward splitting with penalization for monotone inclusion problems"],"prefix":"10.1007","volume":"73","author":[{"given":"Nimit","family":"Nimana","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6539-7107","authenticated-orcid":false,"given":"Narin","family":"Petrot","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,12,15]]},"reference":[{"issue":"6","key":"730_CR1","doi-asserted-by":"publisher","first-page":"1315","DOI":"10.1016\/j.jde.2009.06.014","volume":"248","author":"H Attouch","year":"2010","unstructured":"Attouch, H., Czarnecki, M.-O.: Asymptotic behavior of coupled dynamical systems with multiscale aspects. J. Differ. Equ. 248(6), 1315\u20131344 (2010)","journal-title":"J. Differ. Equ."},{"issue":"1","key":"730_CR2","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1137\/100789464","volume":"21","author":"H Attouch","year":"2011","unstructured":"Attouch, H., Czarnecki, M.-O., Peypouquet, J.: Prox-penalization and splitting methods for constrained variational problems. SIAM J. Optim. 21(1), 149\u2013173 (2011)","journal-title":"SIAM J. Optim."},{"issue":"4","key":"730_CR3","doi-asserted-by":"publisher","first-page":"1251","DOI":"10.1137\/110820300","volume":"21","author":"H Attouch","year":"2011","unstructured":"Attouch, H., Czarnecki, M.-O., Peypouquet, J.: Coupling forward\u2013backward with penalty schemes and parallel splitting for constrained variational inequalities. SIAM J. Optim. 21(4), 1251\u20131274 (2011)","journal-title":"SIAM J. Optim."},{"key":"730_CR4","doi-asserted-by":"publisher","first-page":"1824","DOI":"10.1137\/15M1046095","volume":"26","author":"H Attouch","year":"2016","unstructured":"Attouch, H., Peypouquet, J.: The rate of convergence of Nesterov\u2019s accelerated forward\u2013backward method is actually faster than $$1\/k^2$$ 1 \/ k 2 . SIAM J. Optim. 26, 1824\u20131834 (2016)","journal-title":"SIAM J. Optim."},{"key":"730_CR5","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1007\/BF03007664","volume":"26","author":"J-B Baillon","year":"1977","unstructured":"Baillon, J.-B., Haddad, G.: Quelques propri\u00e9t\u00e9s des op\u00e9rateurs angle-born\u00e9s et $$n$$ n -cycliquement monotones. Israel J. Math. 26, 137\u2013150 (1977)","journal-title":"Israel J. Math."},{"issue":"3","key":"730_CR6","doi-asserted-by":"publisher","first-page":"930","DOI":"10.1007\/s10957-014-0700-x","volume":"166","author":"S Banert","year":"2015","unstructured":"Banert, S., Bo\u0163, R.I.: Backward penalty schemes for monotone inclusion problems. J. Optim. Theory Appl. 166(3), 930\u2013948 (2015)","journal-title":"J. Optim. Theory Appl."},{"key":"730_CR7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-9467-7","volume-title":"Convex Analysis and Monotone Operator Theory in Hilbert Spaces","author":"HH Bauschke","year":"2011","unstructured":"Bauschke, H.H., Combettes, P.L.: Convex Analysis and Monotone Operator Theory in Hilbert Spaces. Springer, New York (2011)"},{"issue":"2","key":"730_CR8","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1137\/16M1080173","volume":"60","author":"L Bottou","year":"2018","unstructured":"Bottou, L., Curtis, F.E., Nocedal, J.: Optimization methods for large-scale machine learning. SIAM Rev. 60(2), 223\u2013311 (2018)","journal-title":"SIAM Rev."},{"issue":"4","key":"730_CR9","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1007\/s10013-013-0050-2","volume":"42","author":"RI Bo\u0163","year":"2014","unstructured":"Bo\u0163, R.I., Csetnek, E.R.: A Tseng\u2019s type penalty scheme for solving inclusion problems involving linearly composed and parallel-sum type monotone operators. Vietnam J. Math. 42(4), 451\u2013465 (2014)","journal-title":"Vietnam J. Math."},{"key":"730_CR10","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1007\/s11228-014-0274-7","volume":"22","author":"RI Bo\u0163","year":"2014","unstructured":"Bo\u0163, R.I., Csetnek, E.R.: Forward\u2013backward and Tseng\u2019s type penalty schemes for monotone inclusion problems. Set-Valued Var. Anal. 22, 313\u2013331 (2014)","journal-title":"Set-Valued Var. Anal."},{"key":"730_CR11","doi-asserted-by":"publisher","first-page":"519","DOI":"10.1007\/s11075-015-0007-5","volume":"71","author":"RI Bo\u0163","year":"2016","unstructured":"Bo\u0163, R.I., Csetnek, E.R.: An inertial forward\u2013backward\u2013forward primal\u2013dual splitting algorithm for solving monotone inclusion problems. Numer. Algorithms 71, 519\u2013540 (2016)","journal-title":"Numer. Algorithms"},{"key":"730_CR12","doi-asserted-by":"publisher","first-page":"965","DOI":"10.1080\/02331934.2016.1181759","volume":"66","author":"RI Bo\u0163","year":"2017","unstructured":"Bo\u0163, R.I., Csetnek, E.R.: Penalty schemes with inertial effects for monotone inclusion problems. Optimization 66, 965\u2013982 (2017)","journal-title":"Optimization"},{"issue":"1","key":"730_CR13","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1007\/s11590-017-1158-1","volume":"12","author":"RI Bo\u0163","year":"2018","unstructured":"Bo\u0163, R.I., Csetnek, E.R., Nimana, N.: Gradient-type penalty method with inertial effects for solving constrained convex optimization problems with smooth data. Optim. Lett. 12(1), 17\u201333 (2018)","journal-title":"Optim. Lett."},{"issue":"1","key":"730_CR14","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1007\/s10013-017-0256-9","volume":"46","author":"RI Bo\u0163","year":"2018","unstructured":"Bo\u0163, R.I., Csetnek, E.R., Nimana, N.: An inertial proximal-gradient penalization scheme for constrained convex optimization problems. Vietnam J. Math. 46(1), 53\u201371 (2018)","journal-title":"Vietnam J. Math."},{"key":"730_CR15","unstructured":"Chen, C., Chan, R.H., MA, S., Yang, J.: Inertial proximal ADMM for linearly constrained separable convex optimization. SIAM J. Imaging Sci. 8(4), 2239\u20132267 (2015)"},{"issue":"4","key":"730_CR16","doi-asserted-by":"publisher","first-page":"2120","DOI":"10.1137\/140980910","volume":"25","author":"C Chen","year":"2015","unstructured":"Chen, C., Ma, S., Yang, J.: A general inertial proximal point algorithm for mixed variational inequality problem. SIAM J. Optim. 25(4), 2120\u20132142 (2015)","journal-title":"SIAM J. Optim."},{"key":"730_CR17","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1007\/s11228-011-0191-y","volume":"20","author":"PL Combettes","year":"2012","unstructured":"Combettes, P.L., Pesquet, J.-C.: Primal\u2013dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum type monotone operators. Set-Valued Var. Anal. 20, 307\u2013330 (2012)","journal-title":"Set-Valued Var. Anal."},{"key":"730_CR18","first-page":"531","volume":"23","author":"M-O Czarnecki","year":"2016","unstructured":"Czarnecki, M.-O., Noun, N., Peypouquet, J.: Splitting forward\u2013backward penalty scheme for constrained variational problems. J. Convex Anal. 23, 531\u2013565 (2016)","journal-title":"J. Convex Anal."},{"key":"730_CR19","unstructured":"Fitzpatrick, S.: Representing monotone operators by convex functions. In: Workshop\/Miniconference on Functional Analysis and Optimization (Canberra, 1988), pp. 59\u201365, Proc. Centre Math. Anal. Austral. Nat. Univ., 20, Austral. Nat. Univ., Canberra (1988)"},{"key":"730_CR20","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1080\/00401706.1970.10488634","volume":"12","author":"AE Hoerl","year":"1970","unstructured":"Hoerl, A.E., Kennard, R.W.: Ridge regression: biased estimation for nonorthogonal problems. Technometrics 12, 55\u201367 (1970)","journal-title":"Technometrics"},{"key":"730_CR21","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1016\/j.compbiolchem.2012.12.008","volume":"43","author":"T Huang","year":"2013","unstructured":"Huang, T., Gong, H., Yang, C., He, Z.: ProteinLasso: a Lasso regression approach to protein inference problem in shotgun proteomics. Comp. Biol. Chem. 43, 46\u201354 (2013)","journal-title":"Comp. Biol. Chem."},{"issue":"2","key":"730_CR22","doi-asserted-by":"publisher","first-page":"829","DOI":"10.1137\/140957639","volume":"25","author":"J Mairal","year":"2015","unstructured":"Mairal, J.: Incremental majorization\u2013minimization optimization with application to large-scale machine learning. SIAM J. Optim. 25(2), 829\u2013855 (2015)","journal-title":"SIAM J. Optim."},{"issue":"3","key":"730_CR23","doi-asserted-by":"publisher","first-page":"787","DOI":"10.1007\/s10957-013-0296-6","volume":"158","author":"N Noun","year":"2013","unstructured":"Noun, N., Peypouquet, J.: Forward\u2013backward penalty scheme for constrained convex minimization without inf-compactness. J. Optim. Theory Appl. 158(3), 787\u2013795 (2013)","journal-title":"J. Optim. Theory Appl."},{"issue":"2","key":"730_CR24","doi-asserted-by":"publisher","first-page":"1388","DOI":"10.1137\/130942954","volume":"7","author":"P Ochs","year":"2014","unstructured":"Ochs, P., Chen, Y., Brox, T., Pock, T.: iPiano: inertial proximal algorithm for non-convex optimization. SIAM J. Imaging Sci. 7(2), 1388\u20131419 (2014)","journal-title":"SIAM J. Imaging Sci."},{"key":"730_CR25","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1016\/0022-247X(79)90234-8","volume":"72","author":"GB Passty","year":"1979","unstructured":"Passty, G.B.: Ergodic convergence to a zero of the sum of monotone operators in Hilbert space. J. Math. Anal. Appl. 72, 383\u2013390 (1979)","journal-title":"J. Math. Anal. Appl."},{"issue":"1","key":"730_CR26","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1007\/s10957-011-9936-x","volume":"153","author":"J Peypouquet","year":"2012","unstructured":"Peypouquet, J.: Coupling the gradient method with a general exterior penalization scheme for convex minimization. J. Optim. Theory Appl. 153(1), 123\u2013138 (2012)","journal-title":"J. Optim. Theory Appl."},{"key":"730_CR27","volume-title":"Introduction to Optimization (Translated from the Russian). Translations Series in Mathematics and Engineering","author":"BT Polyak","year":"1987","unstructured":"Polyak, B.T.: Introduction to Optimization (Translated from the Russian). Translations Series in Mathematics and Engineering. Optimization Software Inc., Publications Division, New York (1987)"},{"key":"730_CR28","doi-asserted-by":"publisher","first-page":"1199","DOI":"10.1137\/120872802","volume":"6","author":"H Raguet","year":"2013","unstructured":"Raguet, H., Fadili, J., Peyr\u00e9, G.: A generalized forward\u2013backward splitting: SIAM. J. Imaging Sci. 6, 1199\u20131226 (2013)","journal-title":"J. Imaging Sci."},{"key":"730_CR29","doi-asserted-by":"publisher","first-page":"2706","DOI":"10.1137\/15M1018253","volume":"8","author":"H Raguet","year":"2015","unstructured":"Raguet, H., Landrieu, L.: Preconditioning of a generalized forward\u2013backward splitting and application to optimization on graphs. SIAM J. Imaging Sci. 8, 2706\u20132739 (2015)","journal-title":"SIAM J. Imaging Sci."},{"issue":"1","key":"730_CR30","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1007\/s10107-016-1030-6","volume":"162","author":"M Schmidt","year":"2017","unstructured":"Schmidt, M., Le Roux, N., Bach, F.: Minimizing finite sums with the stochastic average gradient. Math. Program. 162(1), 83\u2013112 (2017)","journal-title":"Math. Program."},{"key":"730_CR31","doi-asserted-by":"publisher","first-page":"667","DOI":"10.1007\/s10444-011-9254-8","volume":"38","author":"BC V\u0169","year":"2013","unstructured":"V\u0169, B.C.: A splitting algorithm for dual monotone inclusions involving cocoercive operators. Adv. Comput. Math. 38, 667\u2013681 (2013)","journal-title":"Adv. Comput. Math."},{"key":"730_CR32","first-page":"567","volume":"14","author":"S Shalev-Schwartz","year":"2013","unstructured":"Shalev-Schwartz, S., Zhang, T.: Stochastic dual coordinate ascent methods for regularized loss minimization. J. Mach. Learn. Res. 14, 567\u2013599 (2013)","journal-title":"J. Mach. Learn. Res."},{"key":"730_CR33","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","volume":"58","author":"R Tibshirani","year":"1996","unstructured":"Tibshirani, R.: Regression shrinkage and selection via the lasso. J. R. Stat. Soc. Ser. B Stat. Methodol. 58, 267\u2013288 (1996)","journal-title":"J. R. Stat. Soc. Ser. B Stat. Methodol."},{"key":"730_CR34","doi-asserted-by":"publisher","DOI":"10.1142\/5021","volume-title":"Convex Analysis in General Vector Spaces","author":"C Z\u0103linescu","year":"2002","unstructured":"Z\u0103linescu, C.: Convex Analysis in General Vector Spaces. World Scientific, Singapore (2002)"},{"key":"730_CR35","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1111\/j.1467-9868.2005.00503.x","volume":"67","author":"H Zou","year":"2005","unstructured":"Zou, H., Hastie, T.: Regularization and variable selection via the elastic net. J. R. Stat. Soc. Ser. B Stat. Methodol. 67, 301\u2013320 (2005)","journal-title":"J. R. Stat. Soc. Ser. B Stat. Methodol."}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-018-00730-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-018-00730-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-018-00730-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,15]],"date-time":"2024-07-15T13:19:26Z","timestamp":1721049566000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-018-00730-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,15]]},"references-count":35,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019,4]]}},"alternative-id":["730"],"URL":"https:\/\/doi.org\/10.1007\/s10898-018-00730-5","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"type":"print","value":"0925-5001"},{"type":"electronic","value":"1573-2916"}],"subject":[],"published":{"date-parts":[[2018,12,15]]},"assertion":[{"value":"26 October 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 December 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 December 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}