Necessary optimality condition for trilevel optimization problem

Gaoxi Li; Zhongping Wan; Jia-wei Chen; Xiaoke Zhao

doi:10.3934/jimo.2018140

Article Contents

2020, Volume 16, Issue 1: 55-70. Doi: 10.3934/jimo.2018140

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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
* Corresponding author

Received: December 31, 2016

Revised: August 31, 2017

Early access: September 2018

Published: October 2019

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

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Abstract

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.

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Mathematics Subject Classification: 90C46, 90C30, 90C31.

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