Some results on the filter method for nonlinear complementary problems

Journal of inequalities and applications

Guoqiang Wang¹  Jueyu Wang²  Chao Gu² 

[1] College of Fundamental Studies, Shanghai University of Engineering Science, 201620, Shanghai, P.R. China;School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, 201209, Shanghai, P.R. China;

关键词: Inequality constrained optimization;    Filter method;    Nonlinear complementarity problems;    KKT point;    Regular conditions;    90C30;    65K05;   

DOI  :  10.1186/s13660-021-02558-2

来源: Springer

【 摘 要 】

Recent studies show that the filter method has good numerical performance for nonlinear complementary problems (NCPs). Their approach is to reformulate an NCP as a constrained optimization solved by filter algorithms. However, they can only prove that the iterative sequence converges to the KKT point of the constrained optimization. In this paper, we investigate the relation between the KKT point of the constrained optimization and the solution of the NCP. First, we give several sufficient conditions under which the KKT point of the constrained optimization is the solution of the NCP; second, we define regular conditions and regular point which include and generalize the previous results; third, we prove that the level sets of the objective function of the constrained optimization are bounded for a strongly monotone function or a uniform P-function; finally, we present some examples to verify the previous results.

【 授权许可】

CC BY