TY - JOUR
T1 - A family of NCP functions and a descent method for the nonlinear complementarity problem
AU - Chen, Jein Shan
AU - Pan, Shaohua
N1 - Funding Information:
J.-S. Chen is a member of Mathematics Division, National Center for Theoretical Sciences, Taipei Office. J.-S. Chen’s work is partially supported by National Science Council of Taiwan.
PY - 2008/7
Y1 - 2008/7
N2 - In last decades, there has been much effort on the solution and the analysis of the nonlinear complementarity problem (NCP) by reformulating NCP as an unconstrained minimization involving an NCP function. In this paper, we propose a family of new NCP functions, which include the Fischer-Burmeister function as a special case, based on a p-norm with p being any fixed real number in the interval (1,+∞), and show several favorable properties of the proposed functions. In addition, we also propose a descent algorithm that is indeed derivative-free for solving the unconstrained minimization based on the merit functions from the proposed NCP functions. Numerical results for the test problems from MCPLIB indicate that the descent algorithm has better performance when the parameter p decreases in (1,+∞). This implies that the merit functions associated with p (1,2), for example p=1.5, are more effective in numerical computations than the Fischer-Burmeister merit function, which exactly corresponds to p=2.
AB - In last decades, there has been much effort on the solution and the analysis of the nonlinear complementarity problem (NCP) by reformulating NCP as an unconstrained minimization involving an NCP function. In this paper, we propose a family of new NCP functions, which include the Fischer-Burmeister function as a special case, based on a p-norm with p being any fixed real number in the interval (1,+∞), and show several favorable properties of the proposed functions. In addition, we also propose a descent algorithm that is indeed derivative-free for solving the unconstrained minimization based on the merit functions from the proposed NCP functions. Numerical results for the test problems from MCPLIB indicate that the descent algorithm has better performance when the parameter p decreases in (1,+∞). This implies that the merit functions associated with p (1,2), for example p=1.5, are more effective in numerical computations than the Fischer-Burmeister merit function, which exactly corresponds to p=2.
KW - Descent method
KW - Merit function
KW - NCP
KW - NCP function
UR - http://www.scopus.com/inward/record.url?scp=45749154599&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=45749154599&partnerID=8YFLogxK
U2 - 10.1007/s10589-007-9086-0
DO - 10.1007/s10589-007-9086-0
M3 - Article
AN - SCOPUS:45749154599
SN - 0926-6003
VL - 40
SP - 389
EP - 404
JO - Computational Optimization and Applications
JF - Computational Optimization and Applications
IS - 3
ER -