TY - JOUR
T1 - Properties of a family of generalized NCP-functions and a derivative free algorithm for complementarity problems
AU - Hu, Sheng Long
AU - Huang, Zheng Hai
AU - Chen, Jein Shan
N1 - Funding Information:
The second author’s work is partially supported by the National Natural Science Foundation of China (Grant No. 10571134 and No. 10871144) and the Natural Science Foundation of Tianjin (Grant No. 07JCYBJC05200).
Funding Information:
The third author’s work is partially supported by National Science Council of Taiwan.
PY - 2009/8/1
Y1 - 2009/8/1
N2 - In this paper, we propose a new family of NCP-functions and the corresponding merit functions, which are the generalization of some popular NCP-functions and the related merit functions. We show that the new NCP-functions and the corresponding merit functions possess a system of favorite properties. Specially, we show that the new NCP-functions are strongly semismooth, Lipschitz continuous, and continuously differentiable; and that the corresponding merit functions have S C1 property (i.e., they are continuously differentiable and their gradients are semismooth) and L C1 property (i.e., they are continuously differentiable and their gradients are Lipschitz continuous) under suitable assumptions. Based on the new NCP-functions and the corresponding merit functions, we investigate a derivative free algorithm for the nonlinear complementarity problem and discuss its global convergence. Some preliminary numerical results are reported.
AB - In this paper, we propose a new family of NCP-functions and the corresponding merit functions, which are the generalization of some popular NCP-functions and the related merit functions. We show that the new NCP-functions and the corresponding merit functions possess a system of favorite properties. Specially, we show that the new NCP-functions are strongly semismooth, Lipschitz continuous, and continuously differentiable; and that the corresponding merit functions have S C1 property (i.e., they are continuously differentiable and their gradients are semismooth) and L C1 property (i.e., they are continuously differentiable and their gradients are Lipschitz continuous) under suitable assumptions. Based on the new NCP-functions and the corresponding merit functions, we investigate a derivative free algorithm for the nonlinear complementarity problem and discuss its global convergence. Some preliminary numerical results are reported.
KW - Complementarity problem
KW - Derivative free algorithm
KW - Merit function
KW - NCP-function
UR - http://www.scopus.com/inward/record.url?scp=67349124364&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=67349124364&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2008.10.056
DO - 10.1016/j.cam.2008.10.056
M3 - Article
AN - SCOPUS:67349124364
SN - 0377-0427
VL - 230
SP - 69
EP - 82
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
IS - 1
ER -