{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T19:09:08Z","timestamp":1773169748980,"version":"3.50.1"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[1995,11,1]],"date-time":"1995-11-01T00:00:00Z","timestamp":815184000000},"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":[[1995,11]]},"DOI":"10.1007\/bf01592242","type":"journal-article","created":{"date-parts":[[2005,4,28]],"date-time":"2005-04-28T20:01:22Z","timestamp":1114718482000},"page":"17-28","source":"Crossref","is-referenced-by-count":15,"title":["A descent method with linear programming subproblems for nondifferentiable convex optimization"],"prefix":"10.1007","volume":"71","author":[{"given":"Sehun","family":"Kim","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kun-Nyeong","family":"Chang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun-Yeon","family":"Lee","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"CR1","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1007\/BFb0121157","volume":"30","author":"A. Auslender","year":"1987","unstructured":"A. Auslender, \u201cNumerical methods for nondifferentiable convex optimization,\u201dMathematical Programming Study 30 (1987) 102\u2013126.","journal-title":"Mathematical Programming Study"},{"key":"CR2","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1137\/0311049","volume":"11","author":"D.P. Bertsekas","year":"1973","unstructured":"D.P. Bertsekas and S.K. Mitter, \u201cA descent numerical method for optimization problems with nondifferentiable cost functions,\u201dSIAM Journal on Control 11 (1973) 637\u2013652.","journal-title":"SIAM Journal on Control"},{"key":"CR3","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-12603-5","volume-title":"Nondifferentiable Optimization","author":"V.F. Demyanov","year":"1985","unstructured":"V.F. Demyanov and L.V. Vasil'ev,Nondifferentiable Optimization (Optimization Software, New York, 1985)."},{"issue":"2","key":"CR4","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1007\/BF02591883","volume":"30","author":"M. Fukushima","year":"1984","unstructured":"M. Fukushima, \u201cA descent algorithm for nonsmooth convex optimization,\u201dMathematical Programming 30 (2) (1984) 163\u2013175.","journal-title":"Mathematical Programming"},{"issue":"2","key":"CR5","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1007\/BF01583790","volume":"23","author":"M. Gaudioso","year":"1982","unstructured":"M. Gaudioso and M.F. Monaco, \u201cA bundle type approach to the unconstrained minimization of convex nonsmooth functions,\u201dMathematical Programming 23 (2) (1982) 216\u2013226.","journal-title":"Mathematical Programming"},{"issue":"4","key":"CR6","first-page":"703","volume":"8","author":"J.E. Kelly","year":"1960","unstructured":"J.E. Kelly, \u201cThe cutting plane method for solving convex programs,\u201dJournal of the SIAM 8 (4) (1960) 703\u2013712.","journal-title":"Journal of the SIAM"},{"issue":"1","key":"CR7","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1007\/BF01594925","volume":"50","author":"S. Kim","year":"1991","unstructured":"S. Kim and H. Ahn, \u201cConvergence of a generalized subgradient method for nondifferentiable convex optimization,\u201dMathematical Programming 50 (1) (1991) 75\u201380.","journal-title":"Mathematical Programming"},{"issue":"3","key":"CR8","first-page":"359","volume":"49","author":"S. Kim","year":"1991","unstructured":"S. Kim, H. Ahn and S.-C. Cho, \u201cVariable target value subgradient method,\u201dMathematical Programming 49 (3) (1991) 359\u2013369.","journal-title":"Mathematical Programming"},{"key":"CR9","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1137\/0327039","volume":"27","author":"K.C. Kiwiel","year":"1989","unstructured":"K.C. Kiwiel, \u201cAn ellipsoid trust region bundle method for nonsmooth convex minimization,\u201dSIAM Journal on Control and Optimization 27 (1989) 737\u2013757.","journal-title":"SIAM Journal on Control and Optimization"},{"issue":"1","key":"CR10","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 (1) (1990) 105\u2013122.","journal-title":"Mathematical Programming"},{"key":"CR11","volume-title":"\u201cNonsmooth optimization and descent methods,\u201d Research Report RR-78-4, IIASA","author":"C. Lemar\u00e9chal","year":"1977","unstructured":"C. Lemar\u00e9chal, \u201cNonsmooth optimization and descent methods,\u201d Research Report RR-78-4, IIASA (Laxenburg, Austria, 1977)."},{"key":"CR12","volume-title":"Nonsmooth Optimization","year":"1978","unstructured":"C. Lemar\u00e9chal and R. Mifflin, eds.,Nonsmooth Optimization (Pergamon Press, Oxford, 1978)."},{"key":"CR13","doi-asserted-by":"crossref","first-page":"442","DOI":"10.1287\/mnsc.8.4.442","volume":"8","author":"C.E. Lemke","year":"1962","unstructured":"C.E. Lemke, \u201cA method of solution for quadratic programs,\u201dManagement Science 8 (1962) 442\u2013453.","journal-title":"Management Science"},{"key":"CR14","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 Lemarechal's algorithm for nonsmooth minimization,\u201dMathematical Programming Study 17 (1982) 77\u201390.","journal-title":"Mathematical Programming Study"},{"key":"CR15","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/0041-5553(69)90061-5","volume":"9","author":"B.T. Polyak","year":"1969","unstructured":"B.T. Polyak, \u201cMinimization of unsmooth functionals,\u201dComputational Mathematics and Mathematical Physics 9 (1969) 14\u201329.","journal-title":"Computational Mathematics and Mathematical Physics"},{"key":"CR16","doi-asserted-by":"crossref","DOI":"10.1515\/9781400873173","volume-title":"Convex Analysis","author":"R.T. Rockafellar","year":"1970","unstructured":"R.T. Rockafellar,Convex Analysis (Princeton University Press, Princeton, NJ, 1970)."},{"key":"CR17","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1137\/0314056","volume":"14","author":"R.T. Rockafellar","year":"1976","unstructured":"R.T. Rockafellar, \u201cMonotone operators and the proximal point algorithm,\u201dSIAM Journal on Control and Optimization 14 (1976) 877\u2013898.","journal-title":"SIAM Journal on Control and Optimization"},{"key":"CR18","volume-title":"Real Analysis","author":"H.L. Royden","year":"1968","unstructured":"H.L. Royden,Real Analysis (Macmillan, New York, 1968)."},{"key":"CR19","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-82118-9","volume-title":"Minimization Methods for Nondifferentiable Functions","author":"N.Z. Shor","year":"1985","unstructured":"N.Z. Shor,Minimization Methods for Nondifferentiable Functions (Springer, Berlin, 1985)."},{"key":"CR20","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\/BF01592242.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01592242\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01592242","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,3]],"date-time":"2019-05-03T15:47:52Z","timestamp":1556898472000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF01592242"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,11]]},"references-count":20,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1995,11]]}},"alternative-id":["BF01592242"],"URL":"https:\/\/doi.org\/10.1007\/bf01592242","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,11]]}}}