Second-Order Optimality Conditions for Strict Efficiency of Constrained Set-Valued Optimization |
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Authors: | S J Li S K Zhu X B Li |
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Institution: | 1. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China 2. Mathematical Sciences Research Institute in Chongqing, Chongqing University, Chongqing, 401331, China
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Abstract: | In this paper, we propose several second-order derivatives for set-valued maps and discuss their properties. By using these derivatives, we obtain second-order necessary optimality conditions for strict efficiency of a set-valued optimization problem with inclusion constraints in real normed spaces. We also establish second-order sufficient optimality conditions for strict efficiency of the set-valued optimization problem in finite-dimensional normed spaces. As applications, we investigate second-order sufficient and necessary optimality conditions for a strict local efficient solution of order two of a nonsmooth vector optimization problem with an abstract set and a functional constraint. |
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