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General Ekeland's Variational Principle for Set-Valued Mappings |
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| Authors: | Chen G Y Huang X X Hou S H |
| Institution: | (1) Institute of Systems Science, Academia Sinica, Beijing, China;(2) Department of Mathematics and Computer Science, Chongqing Normal University, Chongqing, China;(3) Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China |
| Abstract: | In this paper, we introduce the concept of approximate solutions for set-valued optimization problems. A sufficient condition for the existence of approximate solutions is obtained. A general Ekeland's variational principle for set-valued mappings in complete ordered metric spaces and complete metric spaces are derived. These results are generalizations of results for vector-valued functions in Refs. 1–4. |
| Keywords: | Set-valued optimization variational principle Hausdorff maximality principle |
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