Variational sets: Calculus and applications to nonsmooth vector optimization |
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| Authors: | Nguyen Le Hoang Anh Phan Quoc Khanh |
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| Institution: | a Department of Mathematics, University of Natural Sciences of Hochiminh City, 227 Nguyen Van Cu, District 5, Hochiminh City, Viet Namb Department of Mathematics, International University of Hochiminh City, Linh Trung, Thu Duc, Hochiminh City, Viet Namc Department of Mathematics, College of Science, Cantho University, Ninhkieu District, Cantho City, Viet Nam |
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| Abstract: | We develop elements of calculus of variational sets for set-valued mappings, which were recently introduced in Khanh and Tuan (2008) 1] and 2] to replace generalized derivatives in establishing optimality conditions in nonsmooth optimization. Most of the usual calculus rules, from chain and sum rules to rules for unions, intersections, products and other operations on mappings, are established. Direct applications in stability and optimality conditions for various vector optimization problems are provided. |
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| Keywords: | 49J53 90C29 |
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