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doi: 10.3934/jimo.2018140

## Necessary optimality condition for trilevel optimization problem

 1 School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China 2 School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China

* Corresponding author

Received  January 2017 Revised  September 2017 Published  September 2018

Fund Project: This work was supported by the Natural Science Foundation of China (11871383, 11401487), and the Basic and Advanced Research Project of Chongqing(cstc2016jcyjA0239)

This paper mainly studies the optimality conditions for a class of trilevel optimization problem, of which all levels are nonlinear programs. We firstly transform this problem into an auxiliary bilevel optimization problem by applying KKT approach to the lower-level problem. Then we obtain a necessary optimality condition via the differential calculus of Mordukhovich. Finally, a theorem for existence of optimal solution is derived via Weierstrass Theorem.

Citation: Gaoxi Li, Zhongping Wan, Jia-wei Chen, Xiaoke Zhao. Necessary optimality condition for trilevel optimization problem. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2018140
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