{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,17]],"date-time":"2025-09-17T16:07:54Z","timestamp":1758125274359},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,2,7]],"date-time":"2020-02-07T00:00:00Z","timestamp":1581033600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,2,7]],"date-time":"2020-02-07T00:00:00Z","timestamp":1581033600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2020,5]]},"DOI":"10.1007\/s10589-020-00170-6","type":"journal-article","created":{"date-parts":[[2020,2,7]],"date-time":"2020-02-07T17:02:56Z","timestamp":1581094976000},"page":"125-153","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A discretization algorithm for nonsmooth convex semi-infinite programming problems based on bundle methods"],"prefix":"10.1007","volume":"76","author":[{"given":"Li-Ping","family":"Pang","sequence":"first","affiliation":[]},{"given":"Qi","family":"Wu","sequence":"additional","affiliation":[]},{"given":"Jin-He","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Qiong","family":"Wu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,2,7]]},"reference":[{"key":"170_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-08114-4","volume-title":"Introduction to Nonsmooth Optimization: Theory, Practice and Software","author":"A Bagirov","year":"2014","unstructured":"Bagirov, A., Karmitsa, N., M\u00e4kel\u00e4, M.M.: Introduction to Nonsmooth Optimization: Theory, Practice and Software. Springer, Cham (2014)"},{"key":"170_CR2","doi-asserted-by":"publisher","first-page":"853","DOI":"10.1090\/S0025-5718-1978-0483298-X","volume":"32","author":"I Barrodale","year":"1978","unstructured":"Barrodale, I., Delves, L.M., Mason, J.C.: Linear chebyshev approximation of complex-valued functions. Math. Comput. 32, 853\u2013863 (1978)","journal-title":"Math. Comput."},{"key":"170_CR3","volume-title":"Numerical Optimization: Theoretical and Practical Aspects","author":"JF Bonnans","year":"2006","unstructured":"Bonnans, J.F., Gilbert, J.C., Lemarchal, C., Sagastizbal, C.A.: Numerical Optimization: Theoretical and Practical Aspects. Springer, Berlin (2006)"},{"issue":"8","key":"170_CR4","doi-asserted-by":"publisher","first-page":"2314","DOI":"10.1109\/78.852012","volume":"48","author":"HH Dam","year":"2000","unstructured":"Dam, H.H., Teo, K.L., Nordebo, S., Cantoni, A.: The dual parameterization approach to optimal least square fir filter design subject to maximum error constraints. IEEE Trans. Signal Process. 48(8), 2314\u20132320 (2000)","journal-title":"IEEE Trans. Signal Process."},{"key":"170_CR5","doi-asserted-by":"publisher","first-page":"132","DOI":"10.1007\/978-3-642-68874-4_7","volume-title":"Mathematical Programming the State of the Art","author":"S\u00c5 Gustafson","year":"1983","unstructured":"Gustafson, S.-\u00c5., Kortanek, K.: Semi-infinite programming and applications. In: Bachem, A., Korte, B., Gr\u00f6tschel, M. (eds.) Mathematical Programming the State of the Art, pp. 132\u2013157. Springer, Berlin (1983)"},{"issue":"5","key":"170_CR6","doi-asserted-by":"publisher","first-page":"2442","DOI":"10.1137\/090754595","volume":"20","author":"W Hare","year":"2010","unstructured":"Hare, W., Sagastiz\u00e1bal, C.: A redistributed proximal bundle method for nonconvex optimization. SIAM J. Optim. 20(5), 2442\u20132473 (2010)","journal-title":"SIAM J. Optim."},{"issue":"3","key":"170_CR7","doi-asserted-by":"publisher","first-page":"354","DOI":"10.1007\/BF01582235","volume":"34","author":"R Hettich","year":"1986","unstructured":"Hettich, R.: An implementation of a discretization method for semi-infinite programming. Math. Program. 34(3), 354\u2013361 (1986)","journal-title":"Math. Program."},{"issue":"3","key":"170_CR8","first-page":"380","volume":"35","author":"R Hettich","year":"1993","unstructured":"Hettich, R., Kortanek, K.O.: Semi-infinite programming: theory, methods, and applications. Soc. Ind. Appl. Math. 35(3), 380\u2013429 (1993)","journal-title":"Soc. Ind. Appl. Math."},{"issue":"4","key":"170_CR9","doi-asserted-by":"publisher","first-page":"703","DOI":"10.1137\/0108053","volume":"8","author":"JE Kelley","year":"1960","unstructured":"Kelley, J.E.: The cutting-plane method for solving convex programs. Soc. Ind. Appl. Math. 8(4), 703\u2013712 (1960)","journal-title":"Soc. Ind. Appl. Math."},{"issue":"1","key":"170_CR10","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1007\/BF01582892","volume":"52","author":"KC Kiwiel","year":"1991","unstructured":"Kiwiel, K.C.: Exact penalty functions in proximal bundle methods for constrained convex nondifferentiable minimization. Math. Program. 52(1), 285\u2013302 (1991)","journal-title":"Math. Program."},{"key":"170_CR11","volume-title":"Methods of Descent for Nondifferentiable Optimization","author":"KC Kiwiel","year":"2006","unstructured":"Kiwiel, K.C.: Methods of Descent for Nondifferentiable Optimization, vol. 1133. Springer, Berlin (2006)"},{"issue":"4","key":"170_CR12","doi-asserted-by":"publisher","first-page":"901","DOI":"10.1137\/0803047","volume":"3","author":"KO Kortanek","year":"1993","unstructured":"Kortanek, K.O., No, H.: A central cutting plane algorithm for convex semi-infinite programming problems. SIAM J. Optim. 3(4), 901\u2013918 (1993)","journal-title":"SIAM J. Optim."},{"key":"170_CR13","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1049\/ip-f-2.1990.0026","volume":"137","author":"Z Liu","year":"1990","unstructured":"Liu, Z., Gong, Y.H.: Semi-infinite quadratic optimisation method for the design of robust adaptive array processors. IEE Proc. Radar Signal Process. 137, 177\u2013182 (1990)","journal-title":"IEE Proc. Radar Signal Process."},{"issue":"2","key":"170_CR14","doi-asserted-by":"publisher","first-page":"491","DOI":"10.1016\/j.ejor.2006.08.045","volume":"180","author":"M L\u00f3pez","year":"2007","unstructured":"L\u00f3pez, M., Still, G.: Semi-infinite programming. Eur. J. Oper. Res. 180(2), 491\u2013518 (2007)","journal-title":"Eur. J. Oper. Res."},{"key":"170_CR15","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1007\/s11075-018-0490-6","volume":"80","author":"J Lv","year":"2018","unstructured":"Lv, J., Pang, L.P., Xu, N., Xiao, Z.H.: An infeasible bundle method for nonconvex constrained optimization with application to semi-infinite programming problems. Numer. Algorithms 80, 397\u2013427 (2018)","journal-title":"Numer. Algorithms"},{"issue":"4","key":"170_CR16","doi-asserted-by":"publisher","first-page":"1670","DOI":"10.1137\/130925013","volume":"24","author":"S Mehrotra","year":"2014","unstructured":"Mehrotra, S., Papp, D.: A cutting surface algorithm for semi-infinite convex programming with an application to moment robust optimization. SIAM J. Optim. 24(4), 1670\u20131697 (2014)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"170_CR17","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/s10898-013-0063-0","volume":"60","author":"T Okuno","year":"2014","unstructured":"Okuno, T., Fukushima, M.: Local reduction based SQP-type method for semi-infinite programs with an infinite number of second-order cone constraints. J. Glob. Optim. 60(1), 25\u201348 (2014)","journal-title":"J. Glob. Optim."},{"issue":"3","key":"170_CR18","doi-asserted-by":"publisher","first-page":"1009","DOI":"10.1137\/110839631","volume":"22","author":"T Okuno","year":"2012","unstructured":"Okuno, T., Hayashi, S., Fukushima, M.: A regularized explicit exchange method for semi-infinite programs with an infinite number of conic constraints. SIAM J. Optim. 22(3), 1009\u20131028 (2012)","journal-title":"SIAM J. Optim."},{"issue":"2","key":"170_CR19","doi-asserted-by":"publisher","first-page":"433","DOI":"10.1007\/s10589-015-9810-0","volume":"64","author":"LP Pang","year":"2016","unstructured":"Pang, L.P., Lv, J., Wang, J.H.: Constrained incremental bundle method with partial inexact oracle for nonsmooth convex semi-infinite programming problems. Comput. Optim. Appl. 64(2), 433\u2013465 (2016)","journal-title":"Comput. Optim. Appl."},{"key":"170_CR20","unstructured":"Polyak, B.T.: Subgradient methods: a survey of Soviet research. In: Nonsmooth Optimization (Proceedings of the IIASA Workshop, Laxenburg, 1977), IIASA Proc. Ser., vol. 3, pp. 5\u201329. Pergamon, Oxford (1978)"},{"issue":"2","key":"170_CR21","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1016\/0165-1684(95)00077-Q","volume":"46","author":"A Potchinkov","year":"1995","unstructured":"Potchinkov, A., Reemtsen, R.: The design of fir filters in the complex plane by convex optimization. Sig. Process. 46(2), 127\u2013146 (1995)","journal-title":"Sig. Process."},{"issue":"1","key":"170_CR22","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1137\/040603875","volume":"16","author":"C Sagastiz\u00e1bal","year":"2005","unstructured":"Sagastiz\u00e1bal, C., Solodov, M.: An infeasible bundle method for nonsmooth convex constrained optimization without a penalty function or a filter. SIAM J. Optim. 16(1), 146\u2013169 (2005)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"170_CR23","doi-asserted-by":"publisher","first-page":"121","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), 121\u2013152 (1992)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"170_CR24","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1007\/s101070100239","volume":"91","author":"G Still","year":"2001","unstructured":"Still, G.: Discretization in semi-infinite programming: the rate of convergence. Math. Program. 91(1), 53\u201369 (2001)","journal-title":"Math. Program."},{"issue":"6","key":"170_CR25","doi-asserted-by":"publisher","first-page":"803","DOI":"10.1080\/02331938808843393","volume":"19","author":"R Tichatschke","year":"1988","unstructured":"Tichatschke, R., Nebeling, V.: A cutting-plane method for quadratic semi infinite programming problems. Optimization 19(6), 803\u2013817 (1988)","journal-title":"Optimization"},{"issue":"1","key":"170_CR26","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1023\/B:ANOR.0000004764.76984.30","volume":"124","author":"S \u017dakovi\u0107","year":"2003","unstructured":"\u017dakovi\u0107, S., Rustem, B.: Semi-infinite programming and applications to minimax problems. Ann. Oper. Res. 124(1), 81\u2013110 (2003)","journal-title":"Ann. Oper. Res."},{"issue":"8","key":"170_CR27","doi-asserted-by":"publisher","first-page":"1037","DOI":"10.1080\/01630563.2016.1191033","volume":"37","author":"LP Zhang","year":"2016","unstructured":"Zhang, L.P., Wu, S.Y.: An efficient algorithm for min\u2013max convex semi-infinite programming problems. Numer. Funct. Anal. Optim. 37(8), 1037\u20131053 (2016)","journal-title":"Numer. Funct. Anal. Optim."},{"issue":"6","key":"170_CR28","doi-asserted-by":"publisher","first-page":"2959","DOI":"10.1137\/090767133","volume":"20","author":"LP Zhang","year":"2010","unstructured":"Zhang, L.P., Wu, S.Y., L\u00f3pez, M.A.: A new exchange method for convex semi-infinite programming. SIAM J. Optim. 20(6), 2959\u20132977 (2010)","journal-title":"SIAM J. Optim."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-020-00170-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-020-00170-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-020-00170-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,8]],"date-time":"2021-02-08T22:20:02Z","timestamp":1612822802000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-020-00170-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,7]]},"references-count":28,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,5]]}},"alternative-id":["170"],"URL":"https:\/\/doi.org\/10.1007\/s10589-020-00170-6","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,2,7]]},"assertion":[{"value":"15 November 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 February 2020","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}