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The KKT optimality conditions in a class of generalized convex optimization problems with an interval-valued objective function |
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| Authors: | Jianke Zhang Sanyang Liu Lifeng Li Quanxi Feng |
| Affiliation: | 1. Department of Mathematics, School of Science, Xidian University, Xi’an, China 2. Department of Mathematics, School of Science, Xi’an University of Posts and Telecommunications, Xi’an, China 3. School of Science, Guilin University of Technology, Guilin, China |
| Abstract: | In this paper, we study the Karush–Kuhn–Tucker optimality conditions in a class of nonconvex optimization problems with an interval-valued objective function. Firstly, the concepts of preinvexity and invexity are extended to interval-valued functions. Secondly, several properties of interval-valued preinvex and invex functions are investigated. Thirdly, the KKT optimality conditions are derived for LU-preinvex and invex optimization problems with an interval-valued objective function under the conditions of weakly continuous differentiablity and Hukuhara differentiablity. Finally, the relationships between a class of variational-like inequalities and the interval-valued optimization problems are established. |
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