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Stability for semivectorial bilevel programs

Gaoxi Li, ,School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, China, Liping Tang, Yingquan Huang, Xinmin Yang, ,School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, China, ,School of Mathematics Science, Chongqing Normal University, Chongqing, 401331, China
2017 Journal of Industrial and Management Optimization  

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This paper studies the stability for bilevel program where the lower-level program is a multiobjective programming problem. As we know, the weakly efficient solution mapping for parametric multiobjective program is not generally lower semicontinuous. We first obtain this semicontinuity under a suitable assumption. Then, a new condition for the lower semicontinuity of the efficient solution mapping of this problem is also obtained. Finally, we get the continuities of the value functions and the
more » ... olution set mapping for the upper-level problem based on the semicontinuities of solution mappings for the lower-level parametric multiobjective program. 2020 Mathematics Subject Classification. 90C29, 90C31, 90C33.
doi:10.3934/jimo.2020161 fatcat:xeiwz2vognapjo33cjm2gpcr7q
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Gaoxi Li, ,School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, China, Liping Tang, Yingquan Huang, Xinmin Yang, ,School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, China, ,School of Mathematics Science, Chongqing Normal University, Chongqing, 401331, China. "Stability for semivectorial bilevel programs." Journal of Industrial and Management Optimization 13.1 (2017) 0-0