{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:43:52Z","timestamp":1787341432512,"version":"build-2736575974"},"reference-count":18,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/501100004853","name":"Chinese University of Hong Kong","doi-asserted-by":"publisher","award":["CUHK 14302516"],"award-info":[{"award-number":["CUHK 14302516"]}],"id":[{"id":"10.13039\/501100004853","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004853","name":"Chinese University of Hong Kong","doi-asserted-by":"publisher","award":["CUHK 14304014"],"award-info":[{"award-number":["CUHK 14304014"]}],"id":[{"id":"10.13039\/501100004853","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004853","name":"Chinese University of Hong Kong","doi-asserted-by":"publisher","award":["4053218"],"award-info":[{"award-number":["4053218"]}],"id":[{"id":"10.13039\/501100004853","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11771384"],"award-info":[{"award-number":["11771384"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>When the objective function undergoes both a tilt perturbation and a general parameter perturbation, this paper considers the notions of a fully stable H\u00f6lder minimizer, a uniform H\u00f6lder growth condition, and a fully stable $(q,s)$-minimum, where the last notion reduces to the tilt-stable minimum by Levy, Poliquin, and Rockafellar [ SIAM J. Optim., 10 (2000), pp. 580--604] and the fully H\u00f6lder stable minimum by Mordukhovich and Nghia [ SIAM J. Optim., 24 (2014), pp. 1344--1381] as special cases by taking $(q,s)=(2,2)$ and $(q,s)=(2,1)$, respectively. Under weak-($\\mathcal{B}\\mathcal{C}\\mathcal{Q}$) (a new constraint qualification), by using the techniques of variational analysis, we establish relationships among these notions and provide several characterizations for fully stable $(q,s)$-minima, which improve and generalize some existing results in the recent literature.<\/jats:p>","DOI":"10.1137\/17m113424x","type":"journal-article","created":{"date-parts":[[2018,9,20]],"date-time":"2018-09-20T10:06:42Z","timestamp":1537438002000},"page":"2601-2624","source":"Crossref","is-referenced-by-count":2,"title":["Fully H\u00f6lderian Stable Minimum with Respect to Both Tilt and Parameter Perturbations"],"prefix":"10.1137","volume":"28","author":[{"given":"Xi Yin","family":"Zheng","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiangxing","family":"Zhu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kung Fu","family":"Ng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,9,20]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"J. F. Bonnans and A. Shapiro,\n                      Perturbation Analysis of Optimization Problems\n                      , Springer Ser. Oper. Res., Springer, New York, 2000.","DOI":"10.1007\/978-1-4612-1394-9"},{"key":"atypb2","doi-asserted-by":"crossref","unstructured":"H. H. Bauschke and P. L.Combettes,\n                      Convex Analysis and Monotone Operator Theory in Hilbert Spaces\n                      , CMS Books Math., Springer, New York, 2011.","DOI":"10.1007\/978-1-4419-9467-7"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/120876551"},{"key":"atypb4","first-page":"1165","volume":"21","author":"Drusvyatskiy D.","year":"2014","journal-title":"J. Convex Anal."},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623498348274"},{"key":"atypb6","doi-asserted-by":"crossref","unstructured":"B. S. Mordukhovich,\n                      Variational Analysis and Generalized Differentiation \u016dshape I: Basic Theory\n                      , Grundlehren Math. Wiss. 330, Springer, Berlin, 2006.","DOI":"10.1007\/3-540-31247-1"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2013.03.014"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1137\/130906878"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-013-0739-8"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1137\/15M1036890"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1287\/moor.2014.0669"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1137\/130928637"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1137\/120887722"},{"key":"atypb14","doi-asserted-by":"crossref","unstructured":"R. R. Phelps,\n                      Convex Functions, Monotone Operators and Differentiability\n                      , Lect. 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