Hadamard well-posedness for a set-valued optimization problem |
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Authors: | J. Zeng S. J. Li W. Y. Zhang X. W. Xue |
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Affiliation: | 1. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, China 2. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China 3. Department of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, 610074, China
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Abstract: | In this paper, we introduce a kind of Hadamard well-posedness for a set-valued optimization problem. By virtue of a scalarization function, we obtain some relationships between weak ${(varepsilon, e)}$ -minimizers of the set-valued optimization problem and ${varepsilon}$ -approximate solutions of a scalar optimization problem. Then, we establish a scalarization theorem of P.K. convergence for sequences of set-valued mappings. Based on these results, we also derive a sufficient condition of Hadamard well-posedness for the set-valued optimization problem. |
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