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We introduce the concept of uniform efficiency, characterize it and compare it with the well-known concepts of proper efficiency and normal efficiency. Then we establish the semi-differentiability of the marginal (efficient value) mapping and a formula to compute its semi-derivative at a uniformly efficient value. As an application we derive semi-differentiability of the marginal function for a problem in which the constraint set is given by a system of inequalities, and for a problem whose constraint set is a union of polyhedral convex sets. The results of this paper are not only new in the case of nonconvex multiobjective problems, but they also deepen some existing ones for the convex case.<\/jats:p>","DOI":"10.1137\/16m1092192","type":"journal-article","created":{"date-parts":[[2018,5,8]],"date-time":"2018-05-08T11:53:02Z","timestamp":1525780382000},"page":"1255-1281","source":"Crossref","is-referenced-by-count":15,"title":["Semi-differentiability of the Marginal Mapping in Vector Optimization"],"prefix":"10.1137","volume":"28","author":[{"given":"Dinh The","family":"Luc","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Majid","family":"Soleimani-damaneh","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Moslem","family":"Zamani","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,5,8]]},"reference":[{"key":"atypb1","unstructured":"J. Aubin and H. Frankowska,\n                      Set-valued Analysis\n                      , Mod. Birkha\u0308user Class., Birkha\u0308user, Boston, 1990."},{"key":"atypb2","doi-asserted-by":"crossref","unstructured":"B. Bank, J. Guddat, D. Klatte, B. Kummer, and K. Tammer,\n                      Nonlinear Parametric Optimization\n                      , Akademie-Verlag, Berlin, 1982.","DOI":"10.1007\/978-3-0348-6328-5"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.4064\/dm442-0-1"},{"key":"atypb4","doi-asserted-by":"crossref","unstructured":"J. F. Bonnans and A. Shapiro,\n                      Perturbation Analysis of Optimization Problems\n                      , Springer Ser. Oper. Res. Financ. 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Za\u0306linescu,\n                      Set-Valued Optimization: An Introduction with Applications\n                      , Vector Optim., Springer, Berlin, 2015.","DOI":"10.1007\/978-3-642-54265-7"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1007\/BF02275356"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.11650\/twjm\/1500404767"},{"key":"atypb13","doi-asserted-by":"crossref","unstructured":"D. T. Luc,\n                      Theory of Vector Optimization\n                      , Lecture Notes in Econom. and Math. Systems 319, Springer, Berlin, 1989.","DOI":"10.1007\/978-3-642-50280-4"},{"key":"atypb14","doi-asserted-by":"crossref","unstructured":"D. T. 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Wets,\n                      Variational Analysis\n                      , Grundlehren Math. Wiss. 317, Springer, Berlin, 2009."},{"key":"atypb22","unstructured":"H. Sawaragi, Y Nakayama and T. Tanino,\n                      Theory of Multiobjective Optimization\n                      , Math. Sci. Eng. 176, Elsevier, Amsterdam, 1985."},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1007\/BF00940634"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1007\/s11590-010-0223-9"},{"key":"atypb25","first-page":"307","volume":"8","author":"Sun X. K.","year":"2012","journal-title":"Pac. J. 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