{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:19:46Z","timestamp":1740122386760,"version":"3.37.3"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2019,2,8]],"date-time":"2019-02-08T00:00:00Z","timestamp":1549584000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["GR3367\/4-1","WA922\/8-1"],"award-info":[{"award-number":["GR3367\/4-1","WA922\/8-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2019,5]]},"DOI":"10.1007\/s10898-019-00746-5","type":"journal-article","created":{"date-parts":[[2019,2,8]],"date-time":"2019-02-08T15:49:10Z","timestamp":1549640950000},"page":"121-160","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A proximal method for solving nonlinear minmax location problems with perturbed minimal time functions via conjugate duality"],"prefix":"10.1007","volume":"74","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1139-7504","authenticated-orcid":false,"given":"Sorin-Mihai","family":"Grad","sequence":"first","affiliation":[]},{"given":"Oleg","family":"Wilfer","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,2,8]]},"reference":[{"issue":"2","key":"746_CR1","doi-asserted-by":"publisher","first-page":"559","DOI":"10.1007\/s10957-015-0811-z","volume":"168","author":"NT An","year":"2016","unstructured":"An, N.T., Giles, D., Nam, N.M., Rector, R.B.: The log\u2013exponential smoothing technique and Nesterov\u2019s accelerated gradient method for generalized Sylvester problems. J. Optim. Theory Appl. 168(2), 559\u2013583 (2016)","journal-title":"J. Optim. Theory Appl."},{"key":"746_CR2","doi-asserted-by":"crossref","unstructured":"Bauschke, H.H., Buiy, M.N., Wang, X.: On sums and convex combinations of projectors onto convex sets. arXiv:1802.02287v2 (2018)","DOI":"10.1016\/j.jat.2019.02.001"},{"key":"746_CR3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-48311-5","volume-title":"Convex Analysis and Monotone Operator Theory in Hilbert Spaces, CMS Books in Mathematics","author":"HH Bauschke","year":"2017","unstructured":"Bauschke, H.H., Combettes, P.L.: Convex Analysis and Monotone Operator Theory in Hilbert Spaces, CMS Books in Mathematics, 2nd edn. Springer, New York (2017)","edition":"2"},{"issue":"8","key":"746_CR4","doi-asserted-by":"publisher","first-page":"1797","DOI":"10.1007\/s11590-017-1159-0","volume":"11","author":"A Berger","year":"2017","unstructured":"Berger, A., Grigoriev, A., Panin, A., Winokurow, A.: Location, pricing and the problem of Apollonius. Optim. Lett. 11(8), 1797\u20131805 (2017)","journal-title":"Optim. Lett."},{"key":"746_CR5","doi-asserted-by":"crossref","unstructured":"Bounkhel, M.: Subdifferential properties of minimal time functions associated with set-valued mappings with closed convex graphs in Hausdorff topological vector spaces. J. Funct. Spaces Appl. Article ID 707603, 13 pages (2013)","DOI":"10.1155\/2013\/707603"},{"key":"746_CR6","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-02886-1","volume-title":"Duality in Vector Optimization","author":"RI Bo\u0163","year":"2009","unstructured":"Bo\u0163, R.I., Grad, S.-M., Wanka, G.: Duality in Vector Optimization. Springer, Heidelberg (2009)"},{"issue":"4","key":"746_CR7","doi-asserted-by":"publisher","first-page":"625","DOI":"10.1007\/s10898-008-9282-1","volume":"41","author":"RI Bo\u0163","year":"2008","unstructured":"Bo\u0163, R.I., Wanka, G.: The conjugate of the pointwise maximum of two convex functions revisited. J. Glob. Optim. 41(4), 625\u2013632 (2008)","journal-title":"J. Glob. Optim."},{"issue":"8","key":"746_CR8","doi-asserted-by":"publisher","first-page":"1737","DOI":"10.1007\/s11760-014-0664-1","volume":"9","author":"G Chierchia","year":"2015","unstructured":"Chierchia, G., Pustelnik, N., Pesquet, J.-C., Pesquet-Popescu, B.: Epigraphical projection and proximal tools for solving constrained convex optimization problems. Signal Image Video Process. 9(8), 1737\u20131749 (2015)","journal-title":"Signal Image Video Process."},{"issue":"2","key":"746_CR9","first-page":"519","volume":"24","author":"S-M Grad","year":"2017","unstructured":"Grad, S.-M.: On gauge functions for convex cones with possibly empty interiors. J. Convex Anal. 24(2), 519\u2013524 (2017)","journal-title":"J. Convex Anal."},{"issue":"1","key":"746_CR10","first-page":"43","volume":"2","author":"S-M Grad","year":"2017","unstructured":"Grad, S.-M., Wanka, G., Wilfer, O.: Duality and $$\\varepsilon $$ \u03b5 -optimality conditions for multi-composed optimization problems with applications to fractional and entropy optimization. Pure Appl. Funct. Anal. 2(1), 43\u201363 (2017)","journal-title":"Pure Appl. Funct. Anal."},{"key":"746_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-0265-0","volume-title":"Subdifferentials: Theory and Applications, Mathematics and Its Applications 323","author":"AG Kusraev","year":"1995","unstructured":"Kusraev, A.G., Kutateladze, S.S.: Subdifferentials: Theory and Applications, Mathematics and Its Applications 323. Kluwer, Dordrecht (1995)"},{"issue":"9","key":"746_CR12","first-page":"1729","volume":"17","author":"L Meng","year":"2016","unstructured":"Meng, L., Peng, L., Wen, C.-F.: Fr\u00e9chet and proximal subdifferentials of perturbed minimal time functions. J. Nonlinear Convex Anal. 17(9), 1729\u20131737 (2016)","journal-title":"J. Nonlinear Convex Anal."},{"key":"746_CR13","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-031-02406-1","volume-title":"An Easy Path to Convex Analysis and Applications","author":"BS Mordukhovich","year":"2014","unstructured":"Mordukhovich, B.S., Nam, N.M.: An Easy Path to Convex Analysis and Applications. Morgan and Claypool Publishers, Williston (2014)"},{"issue":"4","key":"746_CR14","doi-asserted-by":"publisher","first-page":"615","DOI":"10.1007\/s10898-009-9446-7","volume":"46","author":"BS Mordukhovich","year":"2010","unstructured":"Mordukhovich, B.S., Nam, N.M.: Limiting subgradients of minimal time functions in Banach spaces. J. Global Optim. 46(4), 615\u2013633 (2010)","journal-title":"J. Global Optim."},{"issue":"4","key":"746_CR15","first-page":"915","volume":"18","author":"BS Mordukhovich","year":"2011","unstructured":"Mordukhovich, B.S., Nam, N.M.: Subgradients of minimal time functions under minimal requirements. J. Convex Anal. 18(4), 915\u2013947 (2011)","journal-title":"J. Convex Anal."},{"issue":"10","key":"746_CR16","doi-asserted-by":"publisher","first-page":"2213","DOI":"10.1080\/02331934.2014.972955","volume":"64","author":"NM Nam","year":"2015","unstructured":"Nam, N.M.: Subdifferential formulas for a class of non-convex infimal convolutions. Optimization 64(10), 2213\u20132222 (2015)","journal-title":"Optimization"},{"issue":"2","key":"746_CR17","first-page":"497","volume":"19","author":"NM Nam","year":"2012","unstructured":"Nam, N.M., An, N.T., Salinas, J.: Applications of convex analysis to the smallest intersecting ball problem. J. Convex Anal. 19(2), 497\u2013518 (2012)","journal-title":"J. Convex Anal."},{"issue":"2","key":"746_CR18","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1007\/s10957-013-0366-9","volume":"160","author":"NM Nam","year":"2014","unstructured":"Nam, N.M., Hoang, N., An, N.T.: Constructions of solutions to generalized Sylvester and Fermat\u2013Torricelli problems for Euclidean balls. J. Optim. Theory Appl. 160(2), 483\u2013509 (2014)","journal-title":"J. Optim. Theory Appl."},{"issue":"2","key":"746_CR19","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1007\/s11228-013-0232-9","volume":"21","author":"NM Nam","year":"2013","unstructured":"Nam, N.M., Z\u0103linescu, C.: Variational analysis of directional minimal time functions and applications to location problems. Set-Valued Var. Anal. 21(2), 405\u2013430 (2013)","journal-title":"Set-Valued Var. Anal."},{"key":"746_CR20","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-8853-9","volume-title":"Introductory Lectures on Convex Optimization: A Basic Course, Applied optimization 87","author":"Y Nesterov","year":"2004","unstructured":"Nesterov, Y.: Introductory Lectures on Convex Optimization: A Basic Course, Applied optimization 87. Kluwer, Dordrecht (2004)"},{"issue":"5","key":"746_CR21","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1142\/S0218195909003039","volume":"19","author":"F Nielsen","year":"2009","unstructured":"Nielsen, F., Nock, R.: Approximating smallest enclosing balls with applications to machine learning. Int. J. Comput. Geom. Appl. 19(5), 389\u2013414 (2009)","journal-title":"Int. J. Comput. Geom. Appl."},{"key":"746_CR22","doi-asserted-by":"publisher","DOI":"10.1515\/9781400873173","volume-title":"Convex Analysis","author":"RT Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)"},{"issue":"1","key":"746_CR23","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1090\/S0002-9947-1966-0192318-X","volume":"123","author":"RT Rockafellar","year":"1966","unstructured":"Rockafellar, R.T.: Level sets and continuity of conjugate convex functions. Trans. Am. Math. Soc. 123(1), 46\u201363 (1966)","journal-title":"Trans. Am. Math. Soc."},{"issue":"4","key":"746_CR24","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1007\/s10898-009-9433-z","volume":"46","author":"JH Wang","year":"2010","unstructured":"Wang, J.H., Li, C., Xu, H.K.: Subdifferentials of perturbed distance function in Banach spaces. J. Glob. Optim. 46(4), 489\u2013501 (2010)","journal-title":"J. Glob. Optim."},{"issue":"2","key":"746_CR25","doi-asserted-by":"publisher","first-page":"288","DOI":"10.1007\/s11750-016-0431-2","volume":"25","author":"G Wanka","year":"2017","unstructured":"Wanka, G., Wilfer, O.: A Lagrange duality approach for multi-composed optimization problems. TOP 25(2), 288\u2013313 (2017)","journal-title":"TOP"},{"issue":"7","key":"746_CR26","doi-asserted-by":"publisher","first-page":"1095","DOI":"10.1080\/02331934.2017.1387549","volume":"67","author":"G Wanka","year":"2018","unstructured":"Wanka, G., Wilfer, O.: Duality results for extended multifacility location problems. Optimization 67(7), 1095\u20131119 (2018)","journal-title":"Optimization"},{"issue":"2","key":"746_CR27","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1007\/s00186-017-0603-3","volume":"86","author":"G Wanka","year":"2017","unstructured":"Wanka, G., Wilfer, O.: Duality results for nonlinear single minimax location problems via multi-composed optimization. Math. Methods Oper. Res. 86(2), 401\u2013439 (2017)","journal-title":"Math. Methods Oper. Res."},{"key":"746_CR28","unstructured":"Wanka, G., Wilfer, O.: Formulae of epigraphical projection for solving minimax location problems, Preprint 2017\u20135. Faculty of Mathematics, Chemnitz University of Technology (2017)"},{"key":"746_CR29","unstructured":"Wilfer, O.: Duality investigations for multi-composed optimization problems with applications in location theory. Ph.D. Thesis, Chemnitz University of Technology (2017)"},{"key":"746_CR30","doi-asserted-by":"publisher","DOI":"10.1142\/5021","volume-title":"Convex Analysis in General Vector Spaces","author":"C Z\u0103linescu","year":"2002","unstructured":"Z\u0103linescu, C.: Convex Analysis in General Vector Spaces. World Scientific, Singapore (2002)"},{"issue":"6","key":"746_CR31","doi-asserted-by":"publisher","first-page":"1921","DOI":"10.1007\/s11590-013-0689-3","volume":"8","author":"Y Zhang","year":"2014","unstructured":"Zhang, Y., He, Y., Jiang, Y.: Subdifferentials of a perturbed minimal time function in normed spaces. Optim. Lett. 8(6), 1921\u20131930 (2014)","journal-title":"Optim. Lett."}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-019-00746-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-019-00746-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-019-00746-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,11]],"date-time":"2022-09-11T16:43:53Z","timestamp":1662914633000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-019-00746-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,8]]},"references-count":31,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,5]]}},"alternative-id":["746"],"URL":"https:\/\/doi.org\/10.1007\/s10898-019-00746-5","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"type":"print","value":"0925-5001"},{"type":"electronic","value":"1573-2916"}],"subject":[],"published":{"date-parts":[[2019,2,8]]},"assertion":[{"value":"10 April 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 January 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 February 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}