{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,22]],"date-time":"2025-05-22T19:46:03Z","timestamp":1747943163874,"version":"3.37.3"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2016,8,31]],"date-time":"2016-08-31T00:00:00Z","timestamp":1472601600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2017,1]]},"DOI":"10.1007\/s10957-016-1001-3","type":"journal-article","created":{"date-parts":[[2016,9,2]],"date-time":"2016-09-02T16:05:57Z","timestamp":1472832357000},"page":"9-32","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Nonlinear Error Bounds via a Change of Function"],"prefix":"10.1007","volume":"172","author":[{"given":"Dominique","family":"Az\u00e9","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3281-619X","authenticated-orcid":false,"given":"Jean-No\u00ebl","family":"Corvellec","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,8,31]]},"reference":[{"key":"1001_CR1","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1007\/s11784-015-0220-9","volume":"16","author":"D Az\u00e9","year":"2014","unstructured":"Az\u00e9, D., Corvellec, J.-N.: Nonlinear local error bounds via a change of metric. J. Fixed Point Theory Appl. 16, 351\u2013372 (2014)","journal-title":"J. Fixed Point Theory Appl."},{"key":"1001_CR2","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1051\/cocv:2004013","volume":"10","author":"D Az\u00e9","year":"2004","unstructured":"Az\u00e9, D., Corvellec, J.-N.: Characterizations of error bounds for lower semicontinuous functions on metric spaces. ESAIM Control Optim. Calc. Var. 10, 409\u2013425 (2004)","journal-title":"ESAIM Control Optim. Calc. Var."},{"key":"1001_CR3","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1007\/s10107-007-0102-z","volume":"114","author":"J-N Corvellec","year":"2008","unstructured":"Corvellec, J.-N., Motreanu, V.V.: Nonlinear error bounds for lower semicontinuous functions on metric spaces. Math. Program., Ser. A 114, 291\u2013319 (2008)","journal-title":"Math. Program., Ser. A"},{"issue":"2002","key":"1001_CR4","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1016\/S0362-546X(01)00129-8","volume":"49","author":"D Az\u00e9","year":"2002","unstructured":"Az\u00e9, D., Corvellec, J.-N., Lucchetti, R.E.: Variational pairs and applications to stability in nonsmooth analysis. Nonlinear Anal. 49(2002), 643\u2013670 (2002)","journal-title":"Nonlinear Anal."},{"key":"1001_CR5","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1137\/040605266","volume":"16","author":"P-A Absil","year":"2005","unstructured":"Absil, P.-A., Mahony, R., Andrews, B.: Convergence of the iterates of descent methods for analytic cost functions. SIAM J. Optim. 16, 531\u2013547 (2005)","journal-title":"SIAM J. Optim."},{"key":"1001_CR6","doi-asserted-by":"crossref","first-page":"3319","DOI":"10.1090\/S0002-9947-09-05048-X","volume":"362","author":"J Bolte","year":"2010","unstructured":"Bolte, J., Daniilidis, A., Ley, O., Mazet, L.: Characterizations of \u0141ojasiewicz inequalities: subgradient flows, talweg, convexity. Trans. Am. Math. Soc. 362, 3319\u20133363 (2010)","journal-title":"Trans. Am. Math. Soc."},{"doi-asserted-by":"crossref","unstructured":"Noll, D., Rondepierre, A.: Convergence of linesearch and trust-region methods using the Kurdyka-\u0141ojasiewicz inequality. In: Computational and Analytical Mathematics, Springer Proc. Math. Stat., vol. 50, pp. 593\u2013611. Springer-Verlag, New York (2013)","key":"1001_CR7","DOI":"10.1007\/978-1-4614-7621-4_27"},{"key":"1001_CR8","first-page":"180","volume":"68","author":"E De Giorgi","year":"1980","unstructured":"De Giorgi, E., Marino, A., Tosques, M.: Problemi di evoluzione in spazi metrici e curve di massima pendenza. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur 68, 180\u2013187 (1980)","journal-title":"Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur"},{"key":"1001_CR9","first-page":"225","volume":"13","author":"D Az\u00e9","year":"2006","unstructured":"Az\u00e9, D.: A unified theory for metric regularity of multifunctions. J. Convex Anal. 13, 225\u2013252 (2006)","journal-title":"J. Convex Anal."},{"key":"1001_CR10","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1016\/0022-247X(74)90025-0","volume":"47","author":"I Ekeland","year":"1974","unstructured":"Ekeland, I.: On the variational principle. J. Math. Anal. Appl. 47, 324\u2013353 (1974)","journal-title":"J. Math. Anal. Appl."},{"key":"1001_CR11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.24033\/bsmf.1418","volume":"79","author":"PC Rosenbloom","year":"1951","unstructured":"Rosenbloom, P.C.: Quelques classes de probl\u00e8mes extr\u00e9maux. Bull. Soc. Math. France 79, 1\u201358 (1951)","journal-title":"Bull. Soc. Math. France"},{"key":"1001_CR12","doi-asserted-by":"crossref","first-page":"263","DOI":"10.6028\/jres.049.027","volume":"49","author":"AJ Hoffman","year":"1952","unstructured":"Hoffman, A.J.: On approximate solutions of systems of linear inequalities. J. Res. Nat. Bur. Stand. 49, 263\u2013265 (1952)","journal-title":"J. Res. Nat. Bur. Stand."},{"key":"1001_CR13","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1090\/S0002-9947-1979-0531969-6","volume":"251","author":"AD Ioffe","year":"1979","unstructured":"Ioffe, A.D.: Regular points of Lipschitz functions. Trans. Am. Math. Soc. 251, 61\u201369 (1979)","journal-title":"Trans. Am. Math. Soc."},{"key":"1001_CR14","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1137\/S1052623402412982","volume":"14","author":"Z Wu","year":"2003","unstructured":"Wu, Z., Ye, J.: First-order and second-order conditions for error bounds. SIAM J. Optim. 14, 621\u2013645 (2003)","journal-title":"SIAM J. Optim."},{"key":"1001_CR15","doi-asserted-by":"crossref","first-page":"1301","DOI":"10.1007\/s11590-013-0648-z","volume":"8","author":"M Chao","year":"2014","unstructured":"Chao, M., Cheng, C.: Linear and nonlinear error bounds for lower semicontinuous functions. Optim. Lett. 8, 1301\u20131312 (2014)","journal-title":"Optim. Lett."},{"key":"1001_CR16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/060675721","volume":"19","author":"HV Ngai","year":"2008","unstructured":"Ngai, H.V., Th\u00e9ra, M.: Error bounds in metric spaces and applications to the perturbation stability of metric regularity. SIAM J. Optim. 19, 1\u201320 (2008)","journal-title":"SIAM J. Optim."},{"key":"1001_CR17","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/s10107-013-0670-z","volume":"139","author":"AD Ioffe","year":"2013","unstructured":"Ioffe, A.D.: Nonlinear regularity models. Math. Program., Ser. B 139, 223\u2013242 (2013)","journal-title":"Math. Program., Ser. B"},{"key":"1001_CR18","doi-asserted-by":"crossref","first-page":"769","DOI":"10.5802\/aif.1638","volume":"48","author":"K Kurdyka","year":"1998","unstructured":"Kurdyka, K.: On gradients of functions definable in o-minimal structures. Ann. Inst. Fourier (Grenoble) 48, 769\u2013783 (1998)","journal-title":"Ann. Inst. Fourier (Grenoble)"},{"doi-asserted-by":"crossref","unstructured":"\u0141ojasiewicz, S.: On semi-analytic and subanalytic geometry. In: Panoramas of Mathematics (Warsaw 1992\/94). Banach Center Publ, vol. 34, pp. 89\u2013104. Polish Acad. Sci, Warsaw (1995)","key":"1001_CR19","DOI":"10.4064\/-34-1-89-104"},{"key":"1001_CR20","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1070\/RM1970v025n01ABEH001255","volume":"25","author":"YuI Lyubich","year":"1970","unstructured":"Lyubich, YuI, Maistrowskii, G.D.: The general theory of relaxation processes for convex functionals. Russ. Math. Surv. 25, 57\u2013117 (1970)","journal-title":"Russ. Math. Surv."},{"key":"1001_CR21","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1007\/s10107-007-0121-9","volume":"116","author":"HV Ngai","year":"2009","unstructured":"Ngai, H.V., Th\u00e9ra, M.: Error bounds for systems of lower semicontinuous functions in Asplund spaces. Math. Program., Ser. B 116, 397\u2013427 (2009)","journal-title":"Math. Program., Ser. B"},{"key":"1001_CR22","series-title":"Springer Series in Operations Research","volume-title":"Finite-Dimensional Variational Inequalities and Complementarity Problems","author":"F Facchinei","year":"2003","unstructured":"Facchinei, F., Pang, J.-S.: Finite-Dimensional Variational Inequalities and Complementarity Problems. Springer Series in Operations Research, vol. I. Springer, New York (2003)"},{"key":"1001_CR23","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/S0294-1449(17)30017-3","volume":"6","author":"A Auslender","year":"1989","unstructured":"Auslender, A.: Well behaved asymptotical convex functions. Ann. Inst. H. Poincar\u00e9, Anal. Non Lin\u00e9aire 6, 101\u2013121 (1989)","journal-title":"Ann. Inst. H. Poincar\u00e9, Anal. Non Lin\u00e9aire"},{"key":"1001_CR24","doi-asserted-by":"crossref","first-page":"263","DOI":"10.2140\/pjm.1999.187.263","volume":"187","author":"J-N Corvellec","year":"1999","unstructured":"Corvellec, J.-N.: Quantitative deformation theorems and critical point theory. Pac. J. Math. 187, 263\u2013279 (1999)","journal-title":"Pac. J. Math."},{"key":"1001_CR25","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1023\/A:1016544301594","volume":"10","author":"J-N Corvellec","year":"2002","unstructured":"Corvellec, J.-N., Hantoute, A.: Homotopical stability of isolated critical points of continuous functionals. Set-Valued Anal. 10, 143\u2013164 (2002)","journal-title":"Set-Valued Anal."},{"unstructured":"Ioffe A.D.: Metric regularity. Theory and applications\u2014a survey. arXiv:1505.07920v1","key":"1001_CR26"},{"key":"1001_CR27","volume-title":"Numerical Methods in Extremal Problems","author":"B Pchenitchny","year":"1978","unstructured":"Pchenitchny, B., Daniline, Y.: Numerical Methods in Extremal Problems. Mir, Moscow (1978)"}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-016-1001-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-016-1001-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-016-1001-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-016-1001-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,13]],"date-time":"2019-09-13T01:08:56Z","timestamp":1568336936000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-016-1001-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,8,31]]},"references-count":27,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,1]]}},"alternative-id":["1001"],"URL":"https:\/\/doi.org\/10.1007\/s10957-016-1001-3","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"type":"print","value":"0022-3239"},{"type":"electronic","value":"1573-2878"}],"subject":[],"published":{"date-parts":[[2016,8,31]]}}}