@article{El-Sobky2024, 
author = {B. El-Sobky and Y. Abo-Elnaga and G. Ashry and M. Zidan},
title = {A nonmonton active interior point trust region algorithm based on CHKS smoothing function for solving nonlinear bilevel programming problems},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {3},
pages = {6528-6554},
keywords = {nonlinear bilevel problem, nonmonton trust-region, CHKS smoothing function, active-set, interior-point},
url = {https://www.sciopen.com/article/10.3934/math.2024318},
doi = {10.3934/math.2024318},
abstract = {In this paper, an approach is suggested to solve nonlinear bilevel programming (NBLP) problems. In the suggested method, we convert the NBLP problem into a standard nonlinear programming problem with complementary constraints by applying the Karush-Kuhn-Tucker condition to the lower-level problem. By using the Chen-Harker-Kanzow-Smale (CHKS) smoothing function, the nonlinear programming problem is successively smoothed. A nonmonton active interior-point trust-region algorithm is introduced to solve the smoothed nonlinear programming problem to obtain an approximately optimal solution to the NBLP problem. Results from simulations on several benchmark problems and a real-world case about a watershed trading decision-making problem show how the effectiveness of the suggested approach in NBLP solution development.}
}