{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,15]],"date-time":"2026-03-15T13:58:43Z","timestamp":1773583123861,"version":"3.50.1"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2021,1,8]],"date-time":"2021-01-08T00:00:00Z","timestamp":1610064000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,1,8]],"date-time":"2021-01-08T00:00:00Z","timestamp":1610064000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11771067"],"award-info":[{"award-number":["11771067"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2021,3]]},"DOI":"10.1007\/s10957-020-01801-y","type":"journal-article","created":{"date-parts":[[2021,1,8]],"date-time":"2021-01-08T07:15:59Z","timestamp":1610090159000},"page":"650-672","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Well-Posedness of Minimization Problems in Contact Mechanics"],"prefix":"10.1007","volume":"188","author":[{"given":"Mircea","family":"Sofonea","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yi-bin","family":"Xiao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,1,8]]},"reference":[{"key":"1801_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-10163-7","volume-title":"Variational inequalities frictional contact problems","author":"A Capatina","year":"2014","unstructured":"Capatina, A.: Variational inequalities frictional contact problems. Springer, New York (2014)"},{"key":"1801_CR2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-66165-5","volume-title":"Inequalities in mechanics and physics","author":"G Duvaut","year":"1976","unstructured":"Duvaut, G., Lions, J.-L.: Inequalities in mechanics and physics. Springer, Berlin (1976)"},{"key":"1801_CR3","doi-asserted-by":"publisher","DOI":"10.1201\/9781420027365","volume-title":"Unilateral contact problems: variational methods and existence Theorems","author":"C Eck","year":"2005","unstructured":"Eck, C., Jaru\u0161ek, J., Krbec, M.: Unilateral contact problems: variational methods and existence Theorems. Chapman\/CRC Press, New York (2005)"},{"key":"1801_CR4","doi-asserted-by":"crossref","unstructured":"Han, W., Sofonea, M.: Quasistatic contact problems in viscoelasticity and viscoplasticity. Studies in Advanced Mathematics 30, American Mathematical Society, Providence, RI\u2013International Press, Somerville, MA(2002)","DOI":"10.1090\/amsip\/030"},{"key":"1801_CR5","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970845","volume-title":"Contact problems in elasticity: a study of variational inequalities and Finite Element Methods","author":"N Kikuchi","year":"1988","unstructured":"Kikuchi, N., Oden, J.T.: Contact problems in elasticity: a study of variational inequalities and Finite Element Methods. SIAM, Philadelphia (1988)"},{"key":"1801_CR6","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5152-1","volume-title":"Inequality problems in mechanics and applications","author":"PD Panagiotopoulos","year":"1985","unstructured":"Panagiotopoulos, P.D.: Inequality problems in mechanics and applications. Birkh\u00e4user, Boston (1985)"},{"key":"1801_CR7","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139104166","volume-title":"Mathematical models in contact mechanics","author":"M Sofonea","year":"2012","unstructured":"Sofonea, M., Matei, A.: Mathematical models in contact mechanics. Cambridge University Press, London (2012)"},{"key":"1801_CR8","volume-title":"Variational-Hemivariational inequalities with applications","author":"M Sofonea","year":"2018","unstructured":"Sofonea, M., Mig\u00f3rski, S.: Variational-Hemivariational inequalities with applications. Chapman & Hall\/CRC Press, London (2018)"},{"key":"1801_CR9","first-page":"631","volume":"6","author":"AN Tykhonov","year":"1966","unstructured":"Tykhonov, A.N.: On the stability of functional optimization problems. USSR Comput. Math. Math. Phys. 6, 631\u2013634 (1966)","journal-title":"USSR Comput. Math. Math. Phys."},{"key":"1801_CR10","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1007\/s001860000100","volume":"53","author":"XX Huang","year":"2001","unstructured":"Huang, X.X.: Extended and strongly extended well-posedness of set-valued optimization problems. Math. Methods Oper. Res. 53, 101\u2013116 (2001)","journal-title":"Math. Methods Oper. Res."},{"key":"1801_CR11","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1137\/040614943","volume":"17","author":"XX Huang","year":"2006","unstructured":"Huang, X.X., Yang, X.Q.: Generalized Levitin-Polyak well-posedness in constrained optimization. SIAM J. Optim. 17, 243\u2013258 (2006)","journal-title":"SIAM J. Optim."},{"key":"1801_CR12","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1112\/S0025579300013152","volume":"36","author":"MM \u010coban","year":"1989","unstructured":"\u010coban, M.M., Kenderov, P.S., Revalski, J.P.: Generic well-posedness of optimization problems in topological spaces. Mathematika 36, 301\u2013324 (1989)","journal-title":"Mathematika"},{"key":"1801_CR13","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1007\/BF00927717","volume":"5","author":"M Furi","year":"1970","unstructured":"Furi, M., Vignoli, A.: About well-posed optimization problems for functionals in metric spaces. J. Optim. Theory Appl. 5, 225\u2013229 (1970)","journal-title":"J. Optim. Theory Appl."},{"key":"1801_CR14","doi-asserted-by":"publisher","first-page":"452","DOI":"10.1007\/BF00927444","volume":"5","author":"M Furi","year":"1970","unstructured":"Furi, M., Vignoli, A.: A characterization of well-posed minimum problems in a complete metric space. J. Optim. Theory Appl. 5, 452\u2013461 (1970)","journal-title":"J. Optim. Theory Appl."},{"key":"1801_CR15","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0084195","volume-title":"Well-posed optimization problems","author":"AL Dontchev","year":"1993","unstructured":"Dontchev, A.L., Zolezzi, T.: Well-posed optimization problems. Springer, Berlin (1993)"},{"key":"1801_CR16","doi-asserted-by":"publisher","DOI":"10.1007\/0-387-31082-7","volume-title":"Convexity and well-posed problems","author":"R Lucchetti","year":"2006","unstructured":"Lucchetti, R.: Convexity and well-posed problems. Springer, New York (2006)"},{"key":"1801_CR17","doi-asserted-by":"publisher","unstructured":"Cai, D.L., Sofonea, M., Xiao, Y.B.: Tykhonov well-posedness of a mixed variational problem. Optimization (2020). https:\/\/doi.org\/10.1080\/02331934.2020.1808646","DOI":"10.1080\/02331934.2020.1808646"},{"key":"1801_CR18","doi-asserted-by":"publisher","first-page":"682","DOI":"10.1016\/j.ejor.2009.04.001","volume":"201","author":"YP Fang","year":"2010","unstructured":"Fang, Y.P., Huang, H.J., Yao, J.C.: Well-posedness by perturbations of mixed variational inequalities in Banach spaces. Eur. J. Oper. Res. 201, 682\u2013692 (2010)","journal-title":"Eur. J. Oper. Res."},{"key":"1801_CR19","doi-asserted-by":"publisher","first-page":"909","DOI":"10.1080\/01630569508816652","volume":"16","author":"D Goeleven","year":"1995","unstructured":"Goeleven, D., Mentagui, D.: Well-posed hemivariational inequalities. Numer. Funct. Anal. Optim. 16, 909\u2013921 (1995)","journal-title":"Numer. Funct. Anal. Optim."},{"key":"1801_CR20","doi-asserted-by":"publisher","unstructured":"Hu, R., Sofonea, M., Xiao, Y.B.: A Tykhonov-type well-posedness concept for elliptic hemivariational inequalities. Z. Angew. Math. Phys. 71, 120 (2020). https:\/\/doi.org\/10.1007\/s00033-020-01337-1","DOI":"10.1007\/s00033-020-01337-1"},{"key":"1801_CR21","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1007\/s10898-008-9310-1","volume":"44","author":"XX Huang","year":"2009","unstructured":"Huang, X.X., Yang, X.Q., Zhu, D.L.: Levitin-Polyak well-posedness of variational inequality problems with functional constraints. J. Glob. Optim. 44, 159\u2013174 (2009)","journal-title":"J. Glob. Optim."},{"key":"1801_CR22","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1080\/01630568108816100","volume":"3","author":"R Lucchetti","year":"1981","unstructured":"Lucchetti, R., Patrone, F.: A characterization of Tyhonov well-posedness for minimum problems, with applications to variational inequalities. Numer. Funct. Anal. Optim. 3, 461\u2013476 (1981)","journal-title":"Numer. Funct. Anal. Optim."},{"key":"1801_CR23","doi-asserted-by":"publisher","unstructured":"Sofonea, M., Xiao, Y.B.: Tykhonov well-posedness of a viscoplastic contact problem. Evol. Equ. Control Theory. 9, 1167\u20131185 (2020). https:\/\/doi.org\/10.3934\/eect.2020048","DOI":"10.3934\/eect.2020048"},{"key":"1801_CR24","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1016\/j.nonrwa.2019.04.005","volume":"50","author":"M Sofonea","year":"2019","unstructured":"Sofonea, M., Xiao, Y.B., Couderc, M.: Optimization problems for a viscoelastic frictional contact problem with unilateral constraints. Nonlinear Anal. Real World Appl. 50, 86\u2013103 (2019)","journal-title":"Nonlinear Anal. Real World Appl."},{"key":"1801_CR25","doi-asserted-by":"publisher","first-page":"1261","DOI":"10.11650\/twjm\/1500406298","volume":"15","author":"YB Xiao","year":"2011","unstructured":"Xiao, Y.B., Huang, N.J., Wong, M.M.: Well-posedness of hemivariational inequalities and inclusion problems. Taiwan. J. Math. 15, 1261\u20131276 (2011)","journal-title":"Taiwan. J. Math."},{"key":"1801_CR26","unstructured":"Xiao, Y.B., Sofonea, M.: Tykhonov triples, well-posedness and convergence results. Carphatian J. Math., In press"},{"key":"1801_CR27","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1007\/s10957-019-01549-0","volume":"183","author":"M Sofonea","year":"2019","unstructured":"Sofonea, M., Xiao, Y.B.: On the well-posedness concept in the sense of Tykhonov. J. Optim. Theory. Appl. 183, 139\u2013157 (2019)","journal-title":"J. Optim. Theory. Appl."},{"key":"1801_CR28","doi-asserted-by":"publisher","first-page":"364","DOI":"10.1016\/j.jmaa.2019.02.046","volume":"475","author":"YB Xiao","year":"2019","unstructured":"Xiao, Y.B., Sofonea, M.: On the optimal control of variational-hemivariational inequalities. J. Math. Anal. Appl. 475, 364\u2013384 (2019)","journal-title":"J. Math. Anal. Appl."},{"key":"1801_CR29","doi-asserted-by":"publisher","unstructured":"Sofonea, M., Xiao, Y.B., Couderc, M.: Optimization problems for elastic contact models with unilateral constraints. Z. Angew. Math. Phys. 70, 1 (2019). https:\/\/doi.org\/10.1007\/s000033-018-1046-2","DOI":"10.1007\/s000033-018-1046-2"},{"key":"1801_CR30","volume-title":"Variational methods and applications","author":"G Dinc\u0103","year":"1980","unstructured":"Dinc\u0103, G.: Variational methods and applications. Technical Publishing House, Bucharest (1980)"},{"key":"1801_CR31","volume-title":"Convex functional analysis","author":"AJ Kurdila","year":"2005","unstructured":"Kurdila, A.J., Zabarankin, M.: Convex functional analysis. Birkh\u00e4user, Basel (2005)"},{"key":"1801_CR32","doi-asserted-by":"publisher","first-page":"510","DOI":"10.1016\/0001-8708(69)90009-7","volume":"3","author":"U Mosco","year":"1968","unstructured":"Mosco, U.: Convergence of convex sets and of solutions of variational inequalities. Adv. Math. 3, 510\u2013585 (1968)","journal-title":"Adv. Math."},{"key":"1801_CR33","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1007\/s00033-019-1173-4","volume":"70","author":"M Sofonea","year":"2019","unstructured":"Sofonea, M., Matei, A., Xiao, Y.B.: Optimal control for a class of mixed variational problems. Z. Angew. Math. Phys. 70, 127 (2019). https:\/\/doi.org\/10.1007\/s00033-019-1173-4","journal-title":"Z. Angew. Math. Phys."},{"key":"1801_CR34","first-page":"499","volume":"13","author":"F L\u00e9n\u00e9","year":"1975","unstructured":"L\u00e9n\u00e9, F.: Sur les mat\u00e9riaux \u00e9lastiques \u00e0 \u00e9nergie de d\u00e9formation non quadratique. J. M\u00e9c. 13, 499\u2013534 (1975)","journal-title":"J. M\u00e9c."},{"key":"1801_CR35","unstructured":"Temam, R.: Probl\u00e8mes math\u00e9matiques en plasticit\u00e9. M\u00e9thodes math\u00e9matiques de l\u2019informatique, 12, Gauthiers Villars, Paris(1983)"},{"key":"1801_CR36","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1515\/anona-2020-0107","volume":"10","author":"DL Cai","year":"2021","unstructured":"Cai, D.L., Sofonea, M., Xiao, Y.B.: Convergence results for elliptic variational-hemivariational inequalities. Adv. Nonlinear Anal. 10, 2\u201323 (2021)","journal-title":"Adv. Nonlinear Anal."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-020-01801-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-020-01801-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-020-01801-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,3]],"date-time":"2021-03-03T12:13:24Z","timestamp":1614773604000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-020-01801-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,8]]},"references-count":36,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,3]]}},"alternative-id":["1801"],"URL":"https:\/\/doi.org\/10.1007\/s10957-020-01801-y","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,8]]},"assertion":[{"value":"21 May 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 December 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 January 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}