A nonmonotone derivative-free algorithm for nonlinear complementarity problems based on the new generalized penalized Fischer–Burmeister merit function

2011 ◽  
Vol 58 (4) ◽  
pp. 573-591
Author(s):  
Jianguang Zhu ◽  
Hongwei Liu ◽  
Changhe Liu ◽  
Weijie Cong
Keyword(s):  
Complementarity Problems ◽  
Merit Function ◽  
Nonlinear Complementarity Problems ◽  
Nonlinear Complementarity ◽  
Derivative Free

SOME PROPERTIES OF A CLASS OF MERIT FUNCTIONS FOR SYMMETRIC CONE COMPLEMENTARITY PROBLEMS

2006 ◽  
Vol 23 (04) ◽  
pp. 473-495 ◽  
Author(s):  
YONG-JIN LIU ◽  
LI-WEI ZHANG ◽  
YIN-HE WANG
Keyword(s):  
Error Bound ◽  
Complementarity Problems ◽  
Symmetric Cone ◽  
Merit Function ◽  
Nonlinear Complementarity Problems ◽  
Global Error ◽  
Merit Functions ◽  
Global Error Bound ◽  
Nonlinear Complementarity

In this paper, we extend a class of merit functions proposed by Kanzow et al. (1997) for linear/nonlinear complementarity problems to Symmetric Cone Complementarity Problems (SCCP). We show that these functions have several interesting properties, and establish a global error bound for the solution to the SCCP as well as the level boundedness of every merit function under some mild assumptions. Moreover, several functions are demonstrated to enjoy these properties.

scholarly journals Penalized NCP-functions for nonlinear complementarity problems and a scaling algorithm

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Jueyu Wang ◽  
Chao Gu ◽  
Guoqiang Wang
Keyword(s):  
Complementarity Problems ◽  
Numerical Results ◽  
Nonlinear Complementarity Problems ◽  
Stationary Points ◽  
Nonlinear Complementarity ◽  
Derivative Free

<p style='text-indent:20px;'>In this paper, we systematically study the properties of penalized NCP-functions in derivative-free algorithms for nonlinear complementarity problems (NCPs), and give some regular conditions for stationary points of penalized NCP-functions to be solutions of NCPs. The main contribution is to unify and generalize previous results. Based on one of above penalized NCP-functions, we analyze a scaling algorithm for NCPs. The numerical results show that the scaling can greatly improve the effectiveness of the algorithm.</p>

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