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- Title
Some results on the filter method for nonlinear complementary problems.
- Authors
Wang, Jueyu; Gu, Chao; Wang, Guoqiang
- Abstract
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.
- Subjects
NONLINEAR equations; COMPLEMENTARITY constraints (Mathematics); FILTERS &; filtration; CONSTRAINED optimization; SET functions; ALGORITHMS
- Publication
Journal of Inequalities & Applications, 2021, Vol 2021, Issue 1, p1
- ISSN
1025-5834
- Publication type
Article
- DOI
10.1186/s13660-021-02558-2