Higher-Order Optimality Conditions for Set-Valued Optimization |
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| Authors: | S. J. Li K. L. Teo X. Q. Yang |
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| Affiliation: | (1) College of Mathematics and Science, Chongqing University, Chongqing, 400044, China;(2) Department of Mathematics and Statistics, Curtin University of Technology, GPO Box U1987, Perth, WA, 6845, Australia;(3) Department of Applied Mathematics, Hong Kong Polytechnic University, Kowloon, Hong Kong |
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| Abstract: | This paper deals with higher-order optimality conditions of set-valued optimization problems. By virtue of the higher-order derivatives introduced in (Aubin and Frankowska, Set-Valued Analysis, Birkhäuser, Boston, [1990]) higher-order necessary and sufficient optimality conditions are obtained for a set-valued optimization problem whose constraint condition is determined by a fixed set. Higher-order Fritz John type necessary and sufficient optimality conditions are also obtained for a set-valued optimization problem whose constraint condition is determined by a set-valued map. |
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| Keywords: | mth-order adjacent set mth-order adjacent derivative Set-valued map mth-order optimality condition |
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