{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:35:08Z","timestamp":1787333708685,"version":"3.56.0"},"reference-count":20,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[2005,1]]},"abstract":"<jats:p>We study the behavior of the minimal sets of a sequence of convex sets $ \\left\\{ A_{n}\\right\\} $ converging to a given set $A.$ The main feature of the present work is the use of convexity properties of the sets $A_{n}$ and $ A$ to obtain upper and lower convergence of the minimal frontiers. We emphasize that we study both Kuratowski--Painlev\u00e9 convergence and Attouch--Wets convergence of minimal sets. Moreover, we prove stability results that hold in a normed linear space ordered by a general cone, in order to deal with the most common spaces ordered by their natural nonnegative orthants (e.g., $C\\left( \\left[ a,b\\right] \\right) ,$ $l^{p}$, and $L^{p}\\left( \\mathbb{R}\\right) $ for $1\\leq p\\leq \\infty $). We also make a comparison with the existing results related to the topics considered in our work.<\/jats:p>","DOI":"10.1137\/030602642","type":"journal-article","created":{"date-parts":[[2005,3,2]],"date-time":"2005-03-02T21:00:22Z","timestamp":1109797222000},"page":"513-526","source":"Crossref","is-referenced-by-count":21,"title":["Convergence of Minimal Sets in Convex Vector Optimization"],"prefix":"10.1137","volume":"15","author":[{"given":"Enrico","family":"Miglierina","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Elena","family":"Molho","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,28]]},"reference":[{"key":"R1","unstructured":"H. Attouch,\n                      Variational Convergence for Functions and Operators\n                      , Pitman, Boston, 1984."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1287\/moor.18.1.173"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/S0362-546X(01)00760-X"},{"key":"R4","first-page":"21","volume":"12","author":"Bednarczuk E. M.","year":"1998","journal-title":"Pliska Stud. Math. Bulgar."},{"key":"R5","doi-asserted-by":"crossref","unstructured":"G. Beer,\n                      Topologies on Closed and Closed Convex Sets\n                      , Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1993.","DOI":"10.1007\/978-94-015-8149-3"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1216\/rmjm\/1181072488"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/0328008"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/0362-546X(88)90091-0"},{"key":"R9","doi-asserted-by":"crossref","unstructured":"M. Ehrgott and X. Gandibleux, eds.\n                      Multiple Criteria Optimization. State of the Art Annotated Bibliographic Surveys\n                      , Kluwer Academic Publishers, Boston, 2002.","DOI":"10.1007\/b101915"},{"key":"R10","unstructured":"A. G\u00f6pfert, H. Riahi, C. Tammer, and C. Z\u0103linescu,\n                      Variational Methods in Partially Ordered Spaces\n                      , CMS Books Math. 17, Springer\u2010Verlag, New York, 2003."},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1007\/BF02191776"},{"key":"R12","doi-asserted-by":"crossref","unstructured":"R. B. Holmes,\n                      Geometric Functional Analysis and Its Applications\n                      , Grad. Texts in Math. 24, Springer\u2010Verlag, New York, 1975.","DOI":"10.1007\/978-1-4684-9369-6"},{"key":"R13","doi-asserted-by":"crossref","unstructured":"D. T. Luc,\n                      Theory of Vector Optimization\n                      , Lecture Notes in Econom. and Math. Systems 319, Springer\u2010Verlag, Berlin, Heidelberg, 1989.","DOI":"10.1007\/978-3-642-50280-4"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1007\/BF01027102"},{"key":"R15","unstructured":"R. Lucchetti and E. Miglierina,\n                      Stability for convex vector optimization problems\n                      , Optimization, to appear."},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1007\/s001860300310"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(86)90209-X"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1007\/BF01027110"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1137\/0326031"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012902411532"}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/030602642","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:18:20Z","timestamp":1787332700000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/030602642"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,1]]},"references-count":20,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2005,1]]}},"alternative-id":["10.1137\/030602642"],"URL":"https:\/\/doi.org\/10.1137\/030602642","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,1]]}}}