{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,21]],"date-time":"2025-09-21T17:56:53Z","timestamp":1758477413985,"version":"3.37.3"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2020,7,20]],"date-time":"2020-07-20T00:00:00Z","timestamp":1595203200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,7,20]],"date-time":"2020-07-20T00:00:00Z","timestamp":1595203200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2020,11]]},"DOI":"10.1007\/s10589-020-00213-y","type":"journal-article","created":{"date-parts":[[2020,7,20]],"date-time":"2020-07-20T15:03:55Z","timestamp":1595257435000},"page":"379-409","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A new method based on the proximal bundle idea and gradient sampling technique for minimizing nonsmooth convex functions"],"prefix":"10.1007","volume":"77","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8576-3119","authenticated-orcid":false,"given":"M.","family":"Maleknia","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3806-9316","authenticated-orcid":false,"given":"M.","family":"Shamsi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,7,20]]},"reference":[{"issue":"1","key":"213_CR1","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1137\/16M1089897","volume":"28","author":"W Ackooij","year":"2018","unstructured":"Ackooij, W., Frangioni, A.: Incremental bundle methods using upper models. SIAM J. Optim. 28(1), 379\u2013410 (2018)","journal-title":"SIAM J. Optim."},{"issue":"2","key":"213_CR2","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1023\/A:1013649822153","volume":"112","author":"A Astorino","year":"2002","unstructured":"Astorino, A., Gaudioso, M.: Polyhedral separability through successive LP. J. Optim. Theory Appl. 112(2), 265\u2013293 (2002)","journal-title":"J. Optim. Theory Appl."},{"key":"213_CR3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-08114-4","volume-title":"Introduction to Nonsmooth Optimization","author":"AM Bagirov","year":"2014","unstructured":"Bagirov, A.M., Karmitsa, N., M\u00e4kel\u00e4, M.M.: Introduction to Nonsmooth Optimization. Springer, Berlin (2014)"},{"key":"213_CR4","volume-title":"Numerical Optimization. Theoretical and Practical Aspects","author":"J Bonnans","year":"2006","unstructured":"Bonnans, J., Gilbert, J., Lemar\u00e9chal, C., Sagastiz\u00e1bal, C.A.: Numerical Optimization. Theoretical and Practical Aspects. Springer, Berlin (2006)"},{"key":"213_CR5","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511804441","volume-title":"Convex Optimization","author":"S Boyd","year":"2004","unstructured":"Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, New York (2004)"},{"key":"213_CR6","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1007\/978-3-030-34910-3_6","volume-title":"Numerical Nonsmooth Optimization: State of the Art Algorithms","author":"JV Burke","year":"2020","unstructured":"Burke, J.V., Curtis, F.E., Lewis, A.S., Overton, M.L., Sim\u00f5es, L.E.A.: Gradient sampling methods for nonsmooth optimization. In: Bagirov, A.M., Gaudioso, M., Karmitsa, N., M\u00e4kel\u00e4, M.M., Taheri, S. (eds.) Numerical Nonsmooth Optimization: State of the Art Algorithms, pp. 201\u2013225. Springer, Cham (2020)"},{"issue":"3","key":"213_CR7","doi-asserted-by":"publisher","first-page":"751","DOI":"10.1137\/030601296","volume":"15","author":"JV Burke","year":"2005","unstructured":"Burke, J.V., Lewis, A.S., Overton, M.L.: A robust gradient sampling algorithm for nonsmooth, nonconvex optimization. SIAM J. Optim. 15(3), 751\u2013779 (2005)","journal-title":"SIAM J. Optim."},{"issue":"2","key":"213_CR8","doi-asserted-by":"publisher","first-page":"474","DOI":"10.1137\/090780201","volume":"22","author":"FE Curtis","year":"2012","unstructured":"Curtis, F.E., Overton, M.L.: A sequential quadratic programming algorithm for nonconvex, nonsmooth constrained optimization. SIAM J. Optim. 22(2), 474\u2013500 (2012)","journal-title":"SIAM J. Optim."},{"issue":"6","key":"213_CR9","doi-asserted-by":"publisher","first-page":"1302","DOI":"10.1080\/10556788.2012.714781","volume":"28","author":"FE Curtis","year":"2013","unstructured":"Curtis, F.E., Que, X.: An adaptive gradient sampling algorithm for nonconvex nonsmooth optimization. Optim. Methods Softw. 28(6), 1302\u20131324 (2013)","journal-title":"Optim. Methods Softw."},{"key":"213_CR10","volume-title":"Measure Theory and Fine Properties of Functions","author":"LC Evans","year":"1992","unstructured":"Evans, L.C., Gariepy, R.F.: Measure Theory and Fine Properties of Functions, Revised edn. CRC Press, Boca Raton (1992)","edition":"Revised"},{"issue":"6","key":"213_CR11","doi-asserted-by":"publisher","first-page":"673","DOI":"10.1080\/10556780410001689225","volume":"19","author":"M Haarala","year":"2004","unstructured":"Haarala, M., Miettinen, K., M\u00e4kel\u00e4, M.M.: New limited memory bundle method for large-scale nonsmooth optimization. Optim. Methods Softw. 19(6), 673\u2013692 (2004)","journal-title":"Optim. Methods Softw."},{"issue":"1","key":"213_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10589-015-9762-4","volume":"63","author":"W Hare","year":"2016","unstructured":"Hare, W., Sagastiz\u00e1bal, C., Solodov, M.: A proximal bundle method for nonsmooth nonconvex functions with inexact information. Comput. Optim. Appl. 63(1), 1\u201328 (2016)","journal-title":"Comput. Optim. Appl."},{"issue":"5","key":"213_CR13","doi-asserted-by":"publisher","first-page":"983","DOI":"10.1080\/10556788.2016.1178262","volume":"31","author":"ES Helou","year":"2016","unstructured":"Helou, E.S., Santos, A.S., Sim\u00f5es, L.E.A.: On the differentiability check in gradient sampling methods. Optim. Methods Softw. 31(5), 983\u20131007 (2016)","journal-title":"Optim. Methods Softw."},{"issue":"3","key":"213_CR14","doi-asserted-by":"publisher","first-page":"673","DOI":"10.1007\/s10589-018-0030-2","volume":"71","author":"ES Helou","year":"2018","unstructured":"Helou, E.S., Santos, A.S., Sim\u00f5es, L.E.A.: A fast gradient and function sampling method for finite-max functions. Comput. Optim. Appl. 71(3), 673\u2013717 (2018)","journal-title":"Comput. Optim. Appl."},{"key":"213_CR15","doi-asserted-by":"publisher","first-page":"320","DOI":"10.1007\/BF02591907","volume":"27","author":"K Kiwiel","year":"1983","unstructured":"Kiwiel, K.: An aggregate subgradient method for nonsmooth convex minimization. Math. Program. 27, 320\u2013341 (1983)","journal-title":"Math. Program."},{"key":"213_CR16","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0074500","volume-title":"Methods of Descent for Nondifferentiable Optimization","author":"KC Kiwiel","year":"1985","unstructured":"Kiwiel, K.C.: Methods of Descent for Nondifferentiable Optimization. Springer, Berlin (1985)"},{"key":"213_CR17","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1007\/BF01585731","volume":"46","author":"KC Kiwiel","year":"1990","unstructured":"Kiwiel, K.C.: Proximity control in bundle methods for convex nondifferentiable minimization. Math. Program. 46, 105\u2013122 (1990)","journal-title":"Math. Program."},{"issue":"2","key":"213_CR18","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1137\/050639673","volume":"18","author":"KC Kiwiel","year":"2007","unstructured":"Kiwiel, K.C.: Convergence of the gradient sampling algorithm for nonsmooth nonconvex optimization. SIAM J. Optim. 18(2), 379\u2013388 (2007)","journal-title":"SIAM J. Optim."},{"issue":"4","key":"213_CR19","doi-asserted-by":"publisher","first-page":"1983","DOI":"10.1137\/090748408","volume":"20","author":"KC Kiwiel","year":"2010","unstructured":"Kiwiel, K.C.: A nonderivative version of the gradient sampling algorithm for nonsmooth nonconvex optimization. SIAM J. Optim. 20(4), 1983\u20131994 (2010)","journal-title":"SIAM J. Optim."},{"key":"213_CR20","volume-title":"Molecular Distance Geometry Problem","author":"C Lavor","year":"2009","unstructured":"Lavor, C., Liberti, L., Maculan, N.: Molecular Distance Geometry Problem, 2nd edn. Springer, New York (2009)","edition":"2"},{"key":"213_CR21","unstructured":"Luk\u0161an, L., Tcma, M., Siska, M., Vl\u010dek, J., Ramesova, N.: Ufo 2002. Interactive system for universal functional optimization. Tech. rep., Institute of Computer Science, Academy of Sciences of the Czech Republic (2002)"},{"issue":"2","key":"213_CR22","first-page":"397","volume":"80","author":"J Lv","year":"2019","unstructured":"Lv, J., Pang, L., Xu, N., et al.: An infeasible bundle method for nonconvex constrained optimization with application to semi-infinite programming problems. Comput. Optim. Appl. 80(2), 397\u2013427 (2019)","journal-title":"Comput. Optim. Appl."},{"key":"213_CR23","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1007\/s10288-019-00404-2","volume":"18","author":"N Mahdavi-Amiri","year":"2019","unstructured":"Mahdavi-Amiri, N., Shaeiri, M.: A conjugate gradient sampling method for nonsmooth optimization. 4OR 18, 73\u201390 (2019)","journal-title":"4OR"},{"key":"213_CR24","doi-asserted-by":"publisher","DOI":"10.1142\/1493","volume-title":"Nonsmooth Optimization: Analysis and Algorithms with Applications to optimal control","author":"MM M\u00e4kel\u00e4","year":"1992","unstructured":"M\u00e4kel\u00e4, M.M., Neittaanm\u00e4ki, P.: Nonsmooth Optimization: Analysis and Algorithms with Applications to optimal control. World Scientific, Singapore (1992)"},{"issue":"3","key":"213_CR25","doi-asserted-by":"publisher","first-page":"965","DOI":"10.1137\/S0036142901389165","volume":"40","author":"M Nikolova","year":"2002","unstructured":"Nikolova, M.: Minimizers of cost-functions involving nonsmooth data-fidelity terms. Application to the processing of outliers. SIAM J. Numer. Anal. 40(3), 965\u2013994 (2002)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1\u20132","key":"213_CR26","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1007\/s10107-014-0809-6","volume":"148","author":"W Oliveira","year":"2014","unstructured":"Oliveira, W., Sagastiz\u00e1bal, C., Lemar\u00e9chal, C.: Convex proximal bundle methods in depth: a unified analysis for inexact oracles. Math. Program. 148(1\u20132), 241\u2013277 (2014)","journal-title":"Math. Program."},{"issue":"1","key":"213_CR27","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1007\/s10107-015-0873-6","volume":"156","author":"W Oliveira","year":"2016","unstructured":"Oliveira, W., Solodov, M.: A doubly stabilized bundle method for nonsmooth convex optimization. Math. Program. 156(1), 125\u2013159 (2016)","journal-title":"Math. Program."},{"key":"213_CR28","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2825-5","volume-title":"Nonsmooth Approach to Optimization Problems with Equilibrium Constraints","author":"J Outrata","year":"1998","unstructured":"Outrata, J., Kocvara, M., Zowe, J.: Nonsmooth Approach to Optimization Problems with Equilibrium Constraints. Springer, Dordrecht (1998)"},{"issue":"1","key":"213_CR29","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1137\/0802008","volume":"2","author":"H Schramm","year":"1992","unstructured":"Schramm, H., Zowe, J.: A version of the bundle idea for minimizing a nonsmooth function: conceptual idea, convergence analysis, numerical results. SIAM J. Optim. 2(1), 105\u2013122 (1992)","journal-title":"SIAM J. Optim."},{"key":"213_CR30","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-82118-9","volume-title":"Minimization Methods for Non-differentiable Functions","author":"NZ Shor","year":"1985","unstructured":"Shor, N.Z.: Minimization Methods for Non-differentiable Functions. Springer, Berlin (1985)"},{"key":"213_CR31","unstructured":"Skaaja, M.: Limited memory BFGS for nonsmooth optimization. Master\u2019s thesis, New York University (2010)"},{"key":"213_CR32","volume-title":"Data Mining: Practical Machine Learning Tools and Techniques","author":"IH Witten","year":"2005","unstructured":"Witten, I.H., Frank, E.: Data Mining: Practical Machine Learning Tools and Techniques, 2nd edn. Elsevier, Amsterdam (2005)","edition":"2"}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-020-00213-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10589-020-00213-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-020-00213-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,19]],"date-time":"2021-07-19T23:36:39Z","timestamp":1626737799000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10589-020-00213-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,20]]},"references-count":32,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2020,11]]}},"alternative-id":["213"],"URL":"https:\/\/doi.org\/10.1007\/s10589-020-00213-y","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"type":"print","value":"0926-6003"},{"type":"electronic","value":"1573-2894"}],"subject":[],"published":{"date-parts":[[2020,7,20]]},"assertion":[{"value":"15 November 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 July 2020","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}