Optimality Conditions and Geometric Properties of a Linear Multilevel Programming Problem with Dominated Objective Functions |
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| Authors: | G. Z. Ruan S. Y. Wang Y. Yamamoto S. S. Zhu |
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| Affiliation: | (1) Department of Mathematics, Xiangtan University, China;(2) Institute of Systems Science, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, China;(3) School of Business Administration, Hunan University, China;(4) Institute of Policy and Planning Sciences, University of Tsukuba, Japan;(5) Department of Management Science, School of Management, Fudan University, China |
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| Abstract: | In this paper, a model of a linear multilevel programming problem with dominated objective functions (LMPPD(l)) is proposed, where multiple reactions of the lower levels do not lead to any uncertainty in the upper-level decision making. Under the assumption that the constrained set is nonempty and bounded, a necessary optimality condition is obtained. Two types of geometric properties of the solution sets are studied. It is demonstrated that the feasible set of LMPPD(l) is neither necessarily composed of faces of the constrained set nor necessarily connected. These properties are different from the existing theoretical results for linear multilevel programming problems. |
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| Keywords: | Bilevel programming multilevel programming upper semicontinuity connectedness |
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