Optimality conditions for pessimistic trilevel optimization problem with middle-level problem being pessimistic

Volume 9, Issue 6, pp 3864--3878 http://dx.doi.org/10.22436/jnsa.009.06.34

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Authors

Gaoxi Li - School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, P. R. China. Zhongping Wan - School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, P. R. China. - Computational Science Hubei Key Laboratory, Wuhan University, Wuhan, 430072, P. R. China. Jia-Wei Chen - School of Mathematics and Statistics, Southwest University, Chongqing, 400715, P. R. China. Xiaoke Zhao - School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, P. R. China.

Abstract

This paper mainly studies the optimality conditions for a class of pessimistic trilevel optimization prob- lem, of which middle-level is a pessimistic problem. We firstly translate this problem into an auxiliary pessimistic bilevel optimization problem, by applying KKT approach for the lower level problem. Then we obtain a necessary optimality condition via the differential calculus of Mordukhovich. Finally, we obtain an existence theorem of optimal solution by direct method.

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Keywords

• Pessimistic trilevel optimization
• bilevel programming
• optimality conditions.

MSC

•  90C33
•  90C30

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