{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:56:15Z","timestamp":1753883775870,"version":"3.41.2"},"reference-count":15,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,8,17]],"date-time":"2012-08-17T00:00:00Z","timestamp":1345161600000},"content-version":"vor","delay-in-days":229,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11001092","2011QC064"],"award-info":[{"award-number":["11001092","2011QC064"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"crossref","award":["11001092","2011QC064"],"award-info":[{"award-number":["11001092","2011QC064"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>Sufficient optimality and sensitivity of a parameterized min\u2010max programming with fixed feasible set are analyzed. Based on Clarke\u2032s subdifferential and Chaney\u2032s second\u2010order directional derivative, sufficient optimality of the parameterized min\u2010max programming is discussed first. Moreover, under a convex assumption on the objective function, a subdifferential computation formula of the marginal function is obtained. The assumptions are satisfied naturally for some application problems. Moreover, the formulae based on these assumptions are concise and convenient for algorithmic purpose to solve the applications.<\/jats:p>","DOI":"10.1155\/2012\/692325","type":"journal-article","created":{"date-parts":[[2012,8,17]],"date-time":"2012-08-17T21:02:14Z","timestamp":1345237334000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Sufficient Optimality and Sensitivity Analysis of a Parameterized Min\u2010Max Programming"],"prefix":"10.1155","volume":"2012","author":[{"given":"Huijuan","family":"Xiong","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu","family":"Xiao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chaohong","family":"Song","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2012,8,17]]},"reference":[{"key":"e_1_2_5_1_2","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623496298534"},{"key":"e_1_2_5_2_2","doi-asserted-by":"publisher","DOI":"10.1023\/B:JOTA.0000006684.67437.c3"},{"key":"e_1_2_5_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-006-9077-1"},{"key":"e_1_2_5_4_2","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012901398393"},{"key":"e_1_2_5_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-007-9228-z"},{"key":"e_1_2_5_6_2","doi-asserted-by":"publisher","DOI":"10.1137\/0322017"},{"key":"e_1_2_5_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1394-9"},{"key":"e_1_2_5_8_2","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144596302644"},{"key":"e_1_2_5_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-007-0120-x"},{"key":"e_1_2_5_10_2","doi-asserted-by":"publisher","DOI":"10.1287\/moor.13.4.660"},{"key":"e_1_2_5_11_2","doi-asserted-by":"crossref","DOI":"10.1142\/1493","volume-title":"Nonsmooth Optimizatin: Analysis and Algorithms with Application to Optimal Control","author":"M\u00e4kel\u00e4 M. 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