{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T19:13:36Z","timestamp":1783451616057,"version":"3.55.0"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"1-3","license":[{"start":{"date-parts":[[1995,7,1]],"date-time":"1995-07-01T00:00:00Z","timestamp":804556800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Programming"],"published-print":{"date-parts":[[1995,7]]},"DOI":"10.1007\/bf01585555","type":"journal-article","created":{"date-parts":[[2005,4,28]],"date-time":"2005-04-28T08:42:17Z","timestamp":1114677737000},"page":"111-147","source":"Crossref","is-referenced-by-count":286,"title":["New variants of bundle methods"],"prefix":"10.1007","volume":"69","author":[{"given":"Claude","family":"Lemar\u00e9chal","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Arkadii","family":"Nemirovskii","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yurii","family":"Nesterov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","reference":[{"key":"CR1","volume-title":"Probl\u00e8mes de Minimax via l'Analyse Convexe et les Inegalit\u00e9s Variationnelles: Th\u00e9orie et Algorithmes, Lecture Notes in Economics and Mathematical Systems","author":"A. Auslender","year":"1972","unstructured":"A. Auslender,Probl\u00e8mes de Minimax via l'Analyse Convexe et les Inegalit\u00e9s Variationnelles: Th\u00e9orie et Algorithmes, Lecture Notes in Economics and Mathematical Systems (Springer, Berlin, 1972)."},{"key":"CR2","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1007\/BF01386389","volume":"1","author":"E.W. Cheney","year":"1959","unstructured":"E.W. Cheney and A.A. Goldstein, \u201cNewton's methods for convex programming and Tchebytcheff approximation,\u201dNumerische Mathematik 1 (1959) 253\u2013268.","journal-title":"Numerische Mathematik"},{"key":"CR3","first-page":"1","volume":"4","author":"Yu.M. Ermoliev","year":"1966","unstructured":"Yu.M. Ermoliev, \u201cMethods for solving nonlinear extremal problems,\u201dCybernetics 4 (1966) 1\u201317 (in Russian).","journal-title":"Cybernetics"},{"key":"CR4","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1007\/BF01584070","volume":"1","author":"M. Held","year":"1971","unstructured":"M. Held and R.M. Karp, \u201cThe traveling-salesman problem and minimum spanning trees: Part II,\u201dMathematical Programming 1 (1971) 6\u201325.","journal-title":"Mathematical Programming"},{"key":"CR5","first-page":"206","volume-title":"Nonlinear Programming","author":"P. Huard","year":"1967","unstructured":"P. Huard, \u201cResolution of mathematical programming problems with nonlinear constraints by the method of centers,\u201d in: J. Abadie, ed.,Nonlinear Programming (North-Holland, Amsterdam, 1967) 206\u2013219."},{"key":"CR6","first-page":"703","volume":"8","author":"J.E. Kelley","year":"1960","unstructured":"J.E. Kelley, \u201cThe cutting plane method for solving convex programs,\u201dJournal of the SIAM 8 (1960) 703\u2013712.","journal-title":"Journal of the SIAM"},{"key":"CR7","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1007\/BF02591907","volume":"27","author":"K.C. Kiwiel","year":"1983","unstructured":"K.C. Kiwiel, \u201cAn aggregate subgradient method for nonsmooth convex minimization,\u201dMathematical Programming 27 (1983) 320\u2013341.","journal-title":"Mathematical Programming"},{"key":"CR8","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1007\/BF01585731","volume":"46","author":"K.C. Kiwiel","year":"1990","unstructured":"K.C. Kiwiel, \u201cProximity control in bundle methods for convex nondifferentiable minimization,\u201dMathematical Programming 46 (1990) 105\u2013122.","journal-title":"Mathematical Programming"},{"key":"CR9","first-page":"765","volume":"12","author":"V.Yu. Lebedev","year":"1977","unstructured":"V.Yu. Lebedev, \u201cOn the convergence of the method of loaded functional as applied to a convex programming problem,\u201dJournal of Numerical Mathematics and Mathematical Physics 12 (1977) 765\u2013768 (in Russian).","journal-title":"Journal of Numerical Mathematics and Mathematical Physics"},{"key":"CR10","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1007\/BFb0120700","volume":"3","author":"C. Lemar\u00e9chal","year":"1975","unstructured":"C. Lemar\u00e9chal, \u201cAn extension of Davidon methods to non-differentiable problems,\u201dMathematical Programming Study 3 (1975) 95\u2013109.","journal-title":"Mathematical Programming Study"},{"key":"CR11","volume-title":"\u201cNonsmooth optimization and descent methods,\u201d Research Report 78-4","author":"C. Lemar\u00e9chal","year":"1978","unstructured":"C. Lemar\u00e9chal, \u201cNonsmooth optimization and descent methods,\u201d Research Report 78-4, IIASA, Laxenburg, Austria, 1978."},{"key":"CR12","volume-title":"\u201cNew variants of bundle methods,\u201d Research Report # 1508","author":"C. Lemar\u00e9chal","year":"1991","unstructured":"C. Lemar\u00e9chal, A. Nemirovskii and Yu. Nesterov, \u201cNew variants of bundle methods,\u201d Research Report # 1508, Institut National de Recherche en Informatique et en Automatique, Le Chesnay, 1991."},{"key":"CR13","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/B978-0-12-468662-5.50015-X","volume-title":"Nonlinear Programming 4","author":"C. Lemar\u00e9chal","year":"1981","unstructured":"C. Lemar\u00e9chal, J.J. Strodiot and A. Bihain, \u201cOn a bundle algorithm for nonsmooth optimization,\u201d in: O.L. Mangasarian, R.R. Meyer and S.M. Robinson, eds.,Nonlinear Programming 4 (Academic Press, New York, 1981) 245\u2013282."},{"key":"CR14","doi-asserted-by":"crossref","first-page":"1260","DOI":"10.1137\/0327064","volume":"27","author":"P. Marcotte","year":"1989","unstructured":"P. Marcotte and J.P. Dussault, \u201cA sequential linear programming algorithm for solving monotone variational inequalities,\u201dSIAM Journal on Control and Optimization 27 (1989) 1260\u20131278.","journal-title":"SIAM Journal on Control and Optimization"},{"key":"CR15","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1007\/BFb0120960","volume":"17","author":"R. Mifflin","year":"1982","unstructured":"R. Mifflin, \u201cA modification and an extension of Lemar\u00e9chal's algorithm for nonsmooth minimization,\u201dMathematical Programming Study 17 (1982) 77\u201390.","journal-title":"Mathematical Programming Study"},{"key":"CR16","volume-title":"Problem Complexity and Method Efficiency in Optimization","author":"A.S. Nemirovskij","year":"1983","unstructured":"A.S. Nemirovskij and D.B. Yudin,Problem Complexity and Method Efficiency in Optimization (Wiley-Interscience, New York, 1983)."},{"key":"CR17","volume-title":"\u201cZQPCVX, a Fortran subroutine for convex programming,\u201d Report NA17","author":"M.J.D. Powell","year":"1983","unstructured":"M.J.D. Powell, \u201cZQPCVX, a Fortran subroutine for convex programming,\u201d Report NA17, DAMTP, Cambridge, 1983."},{"key":"CR18","volume-title":"Numerical Methods for Extremal Problems","author":"B.N. Pshenichny","year":"1978","unstructured":"B.N. Pshenichny and Yu.M. Danilin,Numerical Methods for Extremal Problems (Mir, Moscow, 1978)."},{"key":"CR19","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/BF01404880","volume":"9","author":"S.M. Robinson","year":"1972","unstructured":"S.M. Robinson, \u201cExtension of Newton's method to nonlinear functions with values in a cone,\u201dNumerische Mathematik 9 (1972) 341\u2013347.","journal-title":"Numerische Mathematik"},{"key":"CR20","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1090\/S0002-9947-1970-0282272-5","volume":"149","author":"R.T. Rockafellar","year":"1970","unstructured":"R.T. Rockafellar, \u201cOn the maximality of sums of nonlinear monotone operators,\u201dTransactions of the American Mathematical Society 149 (1970) 75\u201388.","journal-title":"Transactions of the American Mathematical Society"},{"key":"CR21","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1137\/0802008","volume":"2","author":"H. Schramm","year":"1992","unstructured":"H. Schramm and J. Zowe, \u201cA version of the bundle idea for minimizing a non-smooth function: conceptual idea, convergence analysis, numerical results,\u201dSIAM Journal on Optimization 2 (1992) 121\u2013152.","journal-title":"SIAM Journal on Optimization"},{"key":"CR22","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/BFb0120703","volume":"3","author":"P. Wolfe","year":"1975","unstructured":"P. Wolfe, \u201cA method of conjugate subgradients for minimizing nondifferentiable functions,\u201dMathematical Programming Study 3 (1975) 145\u2013173.","journal-title":"Mathematical Programming Study"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01585555.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01585555\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01585555","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,3]],"date-time":"2019-05-03T15:32:28Z","timestamp":1556897548000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF01585555"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,7]]},"references-count":22,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[1995,7]]}},"alternative-id":["BF01585555"],"URL":"https:\/\/doi.org\/10.1007\/bf01585555","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,7]]}}}