{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T02:28:31Z","timestamp":1768444111667,"version":"3.49.0"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2015,11,12]],"date-time":"2015-11-12T00:00:00Z","timestamp":1447286400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Optim Lett"],"published-print":{"date-parts":[[2016,10]]},"DOI":"10.1007\/s11590-015-0969-1","type":"journal-article","created":{"date-parts":[[2015,11,12]],"date-time":"2015-11-12T02:51:18Z","timestamp":1447296678000},"page":"1529-1539","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":44,"title":["Global convergence of a proximal linearized algorithm for difference of convex functions"],"prefix":"10.1007","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4053-8211","authenticated-orcid":false,"given":"Jo\u00e3o Carlos O.","family":"Souza","sequence":"first","affiliation":[]},{"given":"Paulo Roberto","family":"Oliveira","sequence":"additional","affiliation":[]},{"given":"Antoine","family":"Soubeyran","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,11,12]]},"reference":[{"key":"969_CR1","first-page":"154","volume":"4","author":"B Martinet","year":"1970","unstructured":"Martinet, B.: Regularisation d\u2019in\u00e9quations variationelles par approximations succesives. Rev. Fran\u00e7aise d\u2019Inform. Recherche Oper. 4, 154\u2013159 (1970)","journal-title":"Rev. Fran\u00e7aise d\u2019Inform. Recherche Oper."},{"key":"969_CR2","doi-asserted-by":"crossref","first-page":"273","DOI":"10.24033\/bsmf.1625","volume":"93","author":"JJ Moreau","year":"1965","unstructured":"Moreau, J.J.: Proximit\u00e9 et dualit\u00e9 dans un espace Hilbertien. Bull. Soc. Math. France 93, 273\u2013299 (1965)","journal-title":"Bull. Soc. Math. France"},{"key":"969_CR3","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1137\/0314056","volume":"14","author":"RT Rockafellar","year":"1976","unstructured":"Rockafellar, R.T.: Monotone operators and the proximal point algorithm. SIAM J. control. optim. 14, 877\u2013898 (1976)","journal-title":"SIAM J. control. optim."},{"key":"969_CR4","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1023\/A:1008321423879","volume":"13","author":"A Kaplan","year":"1998","unstructured":"Kaplan, A., Tichatschke, R.: Proximal point methods and nonconvex optimization. J. Glob. Optim. 13, 389\u2013406 (1998)","journal-title":"J. Glob. Optim."},{"issue":"1","key":"969_CR5","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1007\/s10107-007-0124-6","volume":"116","author":"W Hare","year":"2009","unstructured":"Hare, W., Sagastiz\u00e1bal, C.: Computing proximal points of nonconvex functions. Math. Program. 116(1), 221\u2013258 (2009)","journal-title":"Math. Program."},{"issue":"1","key":"969_CR6","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1016\/j.jmaa.2006.07.076","volume":"330","author":"RG Otero","year":"2007","unstructured":"Otero, R.G., Iusem, A.N.: Proximal methods in reflexive Banach spaces without monotonicity. J. Math. Anal. Appl. 330(1), 433\u2013450 (2007)","journal-title":"J. Math. Anal. Appl."},{"key":"969_CR7","doi-asserted-by":"crossref","unstructured":"Iusem, A.N., Pennanen, T., Svaiter, B.F.: Inexact variants of the proximal point algorithm without monotonicity. SIAM J. Optim. 13(4), 1080\u20131097 (2003)","DOI":"10.1137\/S1052623401399587"},{"issue":"3","key":"969_CR8","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1007\/s11228-015-0319-6","volume":"23","author":"GC Bento","year":"2015","unstructured":"Bento, G.C., Soubeyran, A.: A generalized inexact proximal point method for nonsmooth functions that satisfies Kurdyka-Lojasiewicz inequality. Set-Valued Var. Anal. 23(3), 501\u2013517 (2015)","journal-title":"Set-Valued Var. Anal."},{"issue":"1\u20132","key":"969_CR9","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/s10107-011-0484-9","volume":"137","author":"H Attouch","year":"2013","unstructured":"Attouch, H., Bolte, J., Svaiter, B.F.: Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized gauss-seidel methods. Math. Program 137(1\u20132), 91\u2013129 (2013)","journal-title":"Math. Program"},{"issue":"4","key":"969_CR10","doi-asserted-by":"crossref","first-page":"816","DOI":"10.1287\/moor.26.4.816.10011","volume":"26","author":"RS Burachik","year":"2001","unstructured":"Burachik, R.S., Svaiter, B.F.: A relative error tolerance for a family of generalized proximal point methods. Math. Oper. Res. 26(4), 816\u2013831 (2001)","journal-title":"Math. Oper. Res."},{"issue":"2","key":"969_CR11","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1007\/s101070050022","volume":"88","author":"MV Solodov","year":"2000","unstructured":"Solodov, M.V., Svaiter, B.F.: Error bounds for proximal point subproblems and associated inexact proximal point algorithms. Math. Program 88(2), 371\u2013389 (2000)","journal-title":"Math. Program"},{"issue":"7\u20138","key":"969_CR12","doi-asserted-by":"crossref","first-page":"1013","DOI":"10.1081\/NFA-100108320","volume":"22","author":"MV Solodov","year":"2001","unstructured":"Solodov, M.V., Svaiter, B.F.: A unified framework for some inexact proximal point algorithms. Numer. Funct. Anal. Optim. 22(7\u20138), 1013\u20131035 (2001)","journal-title":"Numer. Funct. Anal. Optim."},{"issue":"5","key":"969_CR13","doi-asserted-by":"crossref","first-page":"2413","DOI":"10.1137\/090766930","volume":"20","author":"A Zaslavski","year":"2010","unstructured":"Zaslavski, A.: Convergence of a proximal point method in the presence of computational errors in Hilbert spaces. SIAM J. Optim. 20(5), 2413\u20132421 (2010)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"969_CR14","first-page":"1","volume":"172","author":"GC Bento","year":"2015","unstructured":"Bento, G.C., Soubeyran, A.: Generalized inexact proximal algorithms: Routine\u2019s formation with resistance to change, following worthwhile changes. J. Optim. Theory Appl. 172(1), 1\u201316 (2015)","journal-title":"J. Optim. Theory Appl."},{"key":"969_CR15","first-page":"451","volume":"21","author":"W Sun","year":"2003","unstructured":"Sun, W., Sampaio, R.J.B., Candido, M.A.B.: Proximal point algorithm for minimization of DC Functions. J. Comput. Math. 21, 451\u2013462 (2003)","journal-title":"J. Comput. Math."},{"key":"969_CR16","first-page":"475","volume":"24","author":"A Moudafi","year":"2006","unstructured":"Moudafi, A., Maing\u00e9, P.-E.: On the convergence of an approximate proximal method for d.c. functions. J. Comput. Math. 24, 475\u2013480 (2006)","journal-title":"J. Comput. Math."},{"key":"969_CR17","doi-asserted-by":"publisher","unstructured":"Souza, J.C.O., Oliveira, P.R.: A proximal point algorithm for DC functions on Hadamard manifolds. J. Glob. Optim. (2015). doi: 10.1007\/s10898-015-0282-7","DOI":"10.1007\/s10898-015-0282-7"},{"key":"969_CR18","doi-asserted-by":"crossref","first-page":"707","DOI":"10.2140\/pjm.1959.9.707","volume":"9","author":"P Hartman","year":"1959","unstructured":"Hartman, P.: On functions representable as a difference of convex functions. Pac. J. Math. 9, 707\u2013713 (1959)","journal-title":"Pac. J. Math."},{"key":"969_CR19","first-page":"673","volume":"17","author":"I Bomze","year":"2010","unstructured":"Bomze, I., Lemar\u00e9chal, C.: Necessary conditions for local optimality in difference-of-convex programming. J. Convex Anal. 17, 673\u2013680 (2010)","journal-title":"J. Convex Anal."},{"issue":"1","key":"969_CR20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1023\/A:1021765131316","volume":"103","author":"R Horst","year":"1999","unstructured":"Horst, R., Thoai, N.V.: DC programming: overview. J. Optim. Theory Appl. 103(1), 1\u201343 (1999)","journal-title":"J. Optim. Theory Appl."},{"key":"969_CR21","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/978-3-642-45610-7_3","volume":"256","author":"JB Hiriart-Urruty","year":"1986","unstructured":"Hiriart-Urruty, J.B.: Generalized differentiabity, duality and optimization for problems dealing with difference of convex functions, Convexity and Duality in Optimization. Lectur. Notes Econ. Math. Syst 256, 37\u201370 (1986)","journal-title":"Lectur. Notes Econ. Math. Syst"},{"key":"969_CR22","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/S0304-0208(08)72402-2","volume":"129","author":"DT Pham","year":"1986","unstructured":"Pham, D.T., Souad, E.B.: Algorithms for solving a class of nonconvex optimization problems: methods of subgradient. Fermat Days 85: Math. Optim. 129, 249\u2013271 (1986)","journal-title":"Fermat Days 85: Math. Optim."},{"issue":"1","key":"969_CR23","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1007\/s10898-014-0159-1","volume":"61","author":"A Ferrer","year":"2015","unstructured":"Ferrer, A., Bagirov, A., Beliakov, G.: Solving DC programs using the cutting angle method. J. Glob. Optim. 61(1), 71\u201389 (2015)","journal-title":"J. Glob. Optim."},{"key":"969_CR24","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/s10479-004-5022-1","volume":"133","author":"DT Pham","year":"2005","unstructured":"Pham, D.T., An, L.T.H., Akoa, F.: The DC (Difference of Convex Functions) programming and DCA revisited with DC models of real world nonconvex optimization problems. Ann. Oper. Res. 133, 23\u201346 (2005)","journal-title":"Ann. Oper. Res."},{"key":"969_CR25","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/s101070050050","volume":"85","author":"K Holmberg","year":"1999","unstructured":"Holmberg, K., Tuy, H.: A production-transportation problem with stochastic demand and concave production costs. Math. Program. 85, 157\u2013179 (1999)","journal-title":"Math. Program."},{"key":"969_CR26","doi-asserted-by":"crossref","unstructured":"Chen, P.C., Hansen, P., Jaumard, B., Tuy, H.: Solution of the multisource weber and conditional weber problems by d.c. programming. Oper. Res. 46(4), 548\u2013562 (1998)","DOI":"10.1287\/opre.46.4.548"},{"key":"969_CR27","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-02796-7","volume-title":"Convex analysis and minimization algorithms","author":"JB Hiriart-Urruty","year":"1993","unstructured":"Hiriart-Urruty, J.B., Lemar\u00e9chal, C.: Convex analysis and minimization algorithms. Springer, Berlin (1993)"},{"key":"969_CR28","doi-asserted-by":"crossref","DOI":"10.1515\/9781400873173","volume-title":"Convex analysis","author":"RT Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex analysis. Princeton University Press, Princeton, New Jersey (1970)"},{"key":"969_CR29","doi-asserted-by":"crossref","first-page":"633","DOI":"10.1007\/s10898-012-9964-6","volume":"57","author":"I Ginchev","year":"2013","unstructured":"Ginchev, I., Gintcheva, D.: Characterization and recognition of dc functions. J. Glob. Optim. 57, 633\u2013647 (2013)","journal-title":"J. Glob. Optim."},{"key":"969_CR30","doi-asserted-by":"crossref","unstructured":"Burachik, R., Gra\u00f1a Drummond, L.M., Iusem, A.N., Svaiter, B.F.: Full convergence of the steepest descent method with inexact line searches. Optimization 32(2), 137\u2013146 (1995)","DOI":"10.1080\/02331939508844042"},{"key":"969_CR31","unstructured":"Soubeyran, A: Variational rationality. Human behaviors as worthwhile stay and change transitions, possibly ending in traps, before reaching desires. Preprint at GREQAM-AMSE (2015)"},{"key":"969_CR32","unstructured":"Polyak, B.T.: Sharp Minima Institute of Control Sciences Lecture Notes, Moscow, USSR, 1979. Presented at the IIASA workshop on generalized Lagrangians and their applications, IIASA, Laxenburg, Austria (1979)"},{"key":"969_CR33","unstructured":"Ferris, M.C.: Weak sharp minima and penalty functions in mathematical programming. Ph.D. Thesis. University of Cambridge, UK (1988)"},{"key":"969_CR34","doi-asserted-by":"crossref","first-page":"1655","DOI":"10.1137\/120864660","volume":"22","author":"G Li","year":"2012","unstructured":"Li, G., Mordukhovich, B.S.: Holder metric subregularity with applications to proximal point method. SIAM J. Optim. 22, 1655\u20131684 (2012)","journal-title":"SIAM J. Optim."}],"container-title":["Optimization Letters"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-015-0969-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11590-015-0969-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-015-0969-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T13:11:43Z","timestamp":1559394703000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11590-015-0969-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11,12]]},"references-count":34,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2016,10]]}},"alternative-id":["969"],"URL":"https:\/\/doi.org\/10.1007\/s11590-015-0969-1","relation":{},"ISSN":["1862-4472","1862-4480"],"issn-type":[{"value":"1862-4472","type":"print"},{"value":"1862-4480","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,11,12]]}}}