{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T08:23:35Z","timestamp":1769502215313,"version":"3.49.0"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2018,5,26]],"date-time":"2018-05-26T00:00:00Z","timestamp":1527292800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100006502","name":"Defense Sciences Office, DARPA","doi-asserted-by":"publisher","award":["HR0011-14-1-0060"],"award-info":[{"award-number":["HR0011-14-1-0060"]}],"id":[{"id":"10.13039\/100006502","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2019,9]]},"DOI":"10.1007\/s10107-018-1275-3","type":"journal-article","created":{"date-parts":[[2018,5,26]],"date-time":"2018-05-26T01:31:35Z","timestamp":1527298295000},"page":"395-423","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Lopsided convergence: an extension and its quantification"],"prefix":"10.1007","volume":"177","author":[{"given":"Johannes O.","family":"Royset","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Roger J-B","family":"Wets","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,5,26]]},"reference":[{"key":"1275_CR1","volume-title":"Variational Convergence for Functions and Operators, Applicable Mathematics Sciences","author":"H Attouch","year":"1984","unstructured":"Attouch, H.: Variational Convergence for Functions and Operators, Applicable Mathematics Sciences. Pitman, Totowa (1984)"},{"key":"1275_CR2","unstructured":"Attouch, H., Az\u00e9, D., Wets, R.J-B: Convergence of convex-concave saddle functions: continuity properties of the Legendre-Fenchel transform with applications to convex programming and mechanics. Ann. l\u2019Inst. H. Poincar\u00e9 Anal. Nonlin\u00e9aire 5, 537\u2013572 (1988)"},{"key":"1275_CR3","first-page":"657","volume":"296","author":"H Attouch","year":"1983","unstructured":"Attouch, H., Wets, R.J-B: Convergence des points min\/sup et de points fixes. C. R. l\u2019Acad. Sci. Paris 296, 657\u2013660 (1983)","journal-title":"C. R. l\u2019Acad. Sci. Paris"},{"issue":"1","key":"1275_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1090\/S0002-9947-1983-0712247-X","volume":"280","author":"H Attouch","year":"1983","unstructured":"Attouch, H., Wets, R.J-B: A convergence theory for saddle functions. Trans. Am. Math. Soc. 280(1), 1\u201341 (1983)","journal-title":"Trans. Am. Math. Soc"},{"issue":"2","key":"1275_CR5","first-page":"695","volume":"328","author":"H Attouch","year":"1991","unstructured":"Attouch, H., Wets, R.J-B: Quantitative stability of variational systems: I. The epigraphical distance. Trans. Am. Math. Soc. 328(2), 695\u2013729 (1991)","journal-title":"Trans. Am. Math. Soc."},{"key":"1275_CR6","volume-title":"Mathematical Methods of Game and Economic Theory","author":"J-P Aubin","year":"1982","unstructured":"Aubin, J.-P.: Mathematical Methods of Game and Economic Theory. North-Holland, Amsterdam (1982)"},{"key":"1275_CR7","volume-title":"Applied Nonlinear Analysis. Issue 1237 of Pure and Applied Mathematics","author":"J-P Aubin","year":"1984","unstructured":"Aubin, J.-P., Ekeland, I.: Applied Nonlinear Analysis. Issue 1237 of Pure and Applied Mathematics. Wiley, New York (1984)"},{"key":"1275_CR8","volume-title":"Set-Valued Analysis","author":"J-P Aubin","year":"1990","unstructured":"Aubin, J.-P., Frankowska, H.: Set-Valued Analysis. Birkh\u00e4user, Basel (1990)"},{"key":"1275_CR9","volume-title":"Topologies on Closed and Closed Convex Sets, Volume 268 of Mathematics and Its Applications","author":"G Beer","year":"1992","unstructured":"Beer, G.: Topologies on Closed and Closed Convex Sets, Volume 268 of Mathematics and Its Applications. Kluwer, Dordrecht (1992)"},{"issue":"3","key":"1275_CR10","doi-asserted-by":"publisher","first-page":"753","DOI":"10.1090\/S0002-9939-1992-1119262-6","volume":"116","author":"G Beer","year":"1990","unstructured":"Beer, G., Rockafellar, R.T., Wets, R.J-B: A characterization of epi-convergence in terms of convergence of level sets. Proc. Am. Math. Soc. 116(3), 753\u2013761 (1992)","journal-title":"Proc. Am. Math. Soc."},{"key":"1275_CR11","doi-asserted-by":"publisher","DOI":"10.1515\/9781400831050","volume-title":"Robust Optimization","author":"A Ben-Tal","year":"2009","unstructured":"Ben-Tal, A., El Ghaoui, L., Nemirovski, A.: Robust Optimization. Princeton University Press, Princeton (2009)"},{"key":"1275_CR12","doi-asserted-by":"crossref","unstructured":"Deride, J., Jofr\u00e9, A., Wets, R.J-B: Solving deterministic and stochastic equilibrium problems via augmented Walrasian. Comput. Econ. (2018, to appear)","DOI":"10.1007\/s10614-017-9733-1"},{"key":"1275_CR13","volume-title":"Optimization Models","author":"L Ghaoui El","year":"2014","unstructured":"El Ghaoui, L., Calafiore, G.C.: Optimization Models. Cambridge University Press, Cambridge (2014)"},{"issue":"1","key":"1275_CR14","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1007\/s10479-009-0653-x","volume":"175","author":"F Facchinei","year":"2010","unstructured":"Facchinei, F., Kanzow, C.: Generalized Nash equilibrium problems. Ann. Oper. Res. 175(1), 177\u2013221 (2010)","journal-title":"Ann. Oper. Res."},{"issue":"5","key":"1275_CR15","doi-asserted-by":"publisher","first-page":"2228","DOI":"10.1137\/090749499","volume":"20","author":"F Facchinei","year":"2010","unstructured":"Facchinei, F., Kanzow, C.: Penalty methods for the solution of generalized Nash equilibrium problems. SIAM J. Optim. 20(5), 2228\u20132253 (2010)","journal-title":"SIAM J. Optim."},{"key":"1275_CR16","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1007\/0-387-30065-1_8","volume-title":"Large-Scale Nonlinear Optimization","author":"F Facchinei","year":"2006","unstructured":"Facchinei, F., Pang, J.-S.: Exact penalty functions for generalized Nash problems. In: Di Pillo, G., Roma, M. (eds.) Large-Scale Nonlinear Optimization, pp. 115\u2013126. Springer, Berlin (2006)"},{"key":"1275_CR17","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1007\/s10287-004-0010-0","volume":"2","author":"M Fukushima","year":"2005","unstructured":"Fukushima, M., Pang, J.-S.: Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games. CMS 2, 21\u201356 (2005)","journal-title":"CMS"},{"key":"1275_CR18","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1007\/s10107-007-0156-y","volume":"117","author":"G G\u00fcrkan","year":"2009","unstructured":"G\u00fcrkan, G., Pang, J.-S.: Approximations of Nash equilibria. Math. Program. B 117, 223\u2013253 (2009)","journal-title":"Math. Program. B"},{"key":"1275_CR19","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1023\/A:1021022522035","volume":"114","author":"A Jofr\u00e9","year":"2002","unstructured":"Jofr\u00e9, A., Wets, R.J-B: Continuity properties of Walras equilibrium points. Ann. Oper. Res. 114, 229\u2013243 (2002)","journal-title":"Ann. Oper. Res."},{"key":"1275_CR20","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1007\/s10107-007-0122-8","volume":"116","author":"A Jofr\u00e9","year":"2009","unstructured":"Jofr\u00e9, A., Wets, R.J-B: Variational convergence of bivariate functions: lopsided convergence. Math. Program. B 116, 275\u2013295 (2009)","journal-title":"Math. Program. B"},{"issue":"4","key":"1275_CR21","doi-asserted-by":"publisher","first-page":"1952","DOI":"10.1137\/120894695","volume":"24","author":"A Jofr\u00e9","year":"2014","unstructured":"Jofr\u00e9, A., Wets, R.J-B: Variational convergence of bifunctions: motivating applications. SIAM J. Optim. 24(4), 1952\u20131979 (2014)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"1275_CR22","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1142\/S0219198908001741","volume":"10","author":"J Morgan","year":"2008","unstructured":"Morgan, J., Scalzo, V.: Variational stability of social Nash equilibria. Int. Game Theory Rev. 10(1), 17\u201324 (2008)","journal-title":"Int. Game Theory Rev."},{"issue":"4","key":"1275_CR23","doi-asserted-by":"publisher","first-page":"510","DOI":"10.1016\/0001-8708(69)90009-7","volume":"3","author":"U Mosco","year":"1969","unstructured":"Mosco, U.: Convergence of convex sets and of solutions of variational inequalities. Adv. Math. 3(4), 510\u2013585 (1969)","journal-title":"Adv. Math."},{"key":"1275_CR24","doi-asserted-by":"publisher","first-page":"807","DOI":"10.2140\/pjm.1955.5.807","volume":"5","author":"H Nikaido","year":"1955","unstructured":"Nikaido, H., Isoda, K.: Note on noncooperative convex games. Pac. J. Math. 5, 807\u2013815 (1955)","journal-title":"Pac. J. Math."},{"key":"1275_CR25","volume-title":"Convex Analysis. Vol. 28 of Princeton Math. Series","author":"RT Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex Analysis. Vol. 28 of Princeton Math. Series. Princeton University Press, Princeton (1970)"},{"key":"1275_CR26","doi-asserted-by":"crossref","unstructured":"Rockafellar, R.T., Wets, R.J-B: Variational Analysis, Volume 317 of Grundlehren der Mathematischen Wissenschaft, 3rd printing-2009 edition. Springer, Berlin (1998)","DOI":"10.1007\/978-3-642-02431-3"},{"key":"1275_CR27","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-017-1165-0","author":"JO Royset","year":"2018","unstructured":"Royset, J.O.: Approximations and solution estimates in optimization. Math. Program. (2018). \n                              https:\/\/doi.org\/10.1007\/s10107-017-1165-0","journal-title":"Math. Program."},{"issue":"3","key":"1275_CR28","doi-asserted-by":"publisher","first-page":"965","DOI":"10.1007\/s10957-015-0839-0","volume":"169","author":"JO Royset","year":"2016","unstructured":"Royset, J.O., Wets, R.J-B: Optimality functions and lopsided convergence. J. Optim. Theory Appl. 169(3), 965\u2013983 (2016)","journal-title":"J. Optim. Theory Appl."},{"issue":"2","key":"1275_CR29","doi-asserted-by":"publisher","first-page":"1118","DOI":"10.1137\/16M1060704","volume":"27","author":"JO Royset","year":"2017","unstructured":"Royset, J.O., Wets, R.J-B: Variational theory for optimization under stochastic ambiguity. SIAM J. Optim. 27(2), 1118\u20131149 (2017)","journal-title":"SIAM J. Optim."},{"key":"1275_CR30","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-9164-5","volume-title":"Bi-level Strategies in Semi-Infinite Programming","author":"O Stein","year":"2003","unstructured":"Stein, O.: Bi-level Strategies in Semi-Infinite Programming. Kluwer, Dordrecht (2003)"},{"key":"1275_CR31","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1287\/moor.2015.0732","volume":"41","author":"H Sun","year":"2015","unstructured":"Sun, H., Xu, H.: Convergence analysis for distributionally robust optimization and equilibrium problems. Math. Oper. Res. 41, 377\u2013401 (2015)","journal-title":"Math. Oper. Res."},{"key":"1275_CR32","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1090\/S0002-9939-1967-0209806-6","volume":"18","author":"D Walkup","year":"1967","unstructured":"Walkup, D., Wets, R.J-B: Continuity of some convex-cone-valued mappings. Proc. Am. Math. Soc. 18, 229\u2013235 (1967)","journal-title":"Proc. Am. Math. Soc."},{"issue":"3","key":"1275_CR33","doi-asserted-by":"publisher","first-page":"1855","DOI":"10.1137\/15M1038529","volume":"26","author":"J Zhang","year":"2016","unstructured":"Zhang, J., Xu, H., Zhang, L.: Quantitative stability analysis for distributionally robust optimization with moment constraints. SIAM J. Optim. 26(3), 1855\u20131882 (2016)","journal-title":"SIAM J. Optim."}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-018-1275-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-018-1275-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-018-1275-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,20]],"date-time":"2019-09-20T10:46:00Z","timestamp":1568976360000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-018-1275-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,26]]},"references-count":33,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2019,9]]}},"alternative-id":["1275"],"URL":"https:\/\/doi.org\/10.1007\/s10107-018-1275-3","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,5,26]]},"assertion":[{"value":"23 August 2016","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 April 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 May 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}