A new semismooth Newton method for solving finite-dimensional quasi-variational inequalities

Journal of inequalities and applications

Zhe Sun¹  Shui-Lian Xie²  Hong-Ru Xu² 

[1] College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, China;School of Mathematics, Jiaying University, 514015, Meizhou, China;

关键词: Quasi-variational inequality;    KKT condition;    Semismooth Newton method;    65K10;    90C53;    90C33;   

DOI  :  10.1186/s13660-021-02671-2

来源: Springer

【 摘 要 】

In this paper, we consider the numerical method for solving finite-dimensional quasi-variational inequalities with both equality and inequality constraints. Firstly, we present a semismooth equation reformulation to the KKT system of a finite-dimensional quasi-variational inequality. Then we propose a semismooth Newton method to solve the equations and establish its global convergence. Finally, we report some numerical results to show the efficiency of the proposed method. Our method can obtain the solution to some problems that cannot be solved by the method proposed in (Facchinei et al. in Comput. Optim. Appl. 62:85–109, 2015). Besides, our method outperforms than the interior point method proposed in (Facchinei et al. in Math. Program. 144:369–412, 2014).

【 授权许可】

CC BY