@article{El-Sobky2023, 
author = {B. El-Sobky and M. F. Zidan},
title = {A trust-region based an active-set interior-point algorithm for fuzzy continuous Static Games},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {6},
pages = {13706-13724},
keywords = {fuzzy continuous static game, active-set, interior-point, trust-region, reduced Hessian technique},
url = {https://www.sciopen.com/article/10.3934/math.2023696},
doi = {10.3934/math.2023696},
abstract = {In this paper, a novel treatment for fuzzy continuous static games (FCSGs) is introduced. This treatment is based on the fact that, as well as having a fuzzy number, the fuzziness is applied to the control vectors to deal with high vagueness and imprecision in a continuous static game. The concept of the    α-level set used for converting the FCSGs to a deterministic problem    α-FCSGs. An active-set strategy is used with Newton's interior point method and a trust-region strategy to insure global convergence for deterministic    α-FCSGs problems from any starting point. A reduced Hessian technique is used to overcome the difficulty of having an infeasible trust-region subproblem. The active-set interior-point trust-region algorithm has new features; it is easy to implement and has rapid convergence. Preliminary numerical results are reported.}
}