Merit functions for nonsmooth complementarity problems and related descent algorithm

2010 ◽  
Vol 25 (1) ◽  
pp. 78-84 ◽  
Author(s):  
Shou-qiang Du ◽  
Yan Gao
Keyword(s):  
Complementarity Problems ◽  
Merit Functions ◽  
Descent Algorithm

scholarly journals Further Application ofH-Differentiability to Generalized Complementarity Problems Based on Generalized Fisher-Burmeister Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Wei-Zhe Gu ◽  
Mohamed A. Tawhid
Keyword(s):  
Stationary Point ◽  
Complementarity Problem ◽  
Global Minimum ◽  
Complementarity Problems ◽  
Merit Function ◽  
Merit Functions ◽  
Generalized Complementarity Problem ◽  
Nonlinear Complementarity ◽  
Generalized Complementarity Problems ◽  
The Given

We study nonsmooth generalized complementarity problems based on the generalized Fisher-Burmeister function and its generalizations, denoted by GCP(f,g) wherefandgareH-differentiable. We describeH-differentials of some GCP functions based on the generalized Fisher-Burmeister function and its generalizations, and their merit functions. Under appropriate conditions on theH-differentials offandg, we show that a local/global minimum of a merit function (or a “stationary point” of a merit function) is coincident with the solution of the given generalized complementarity problem. When specializing GCP(f,g)to the nonlinear complementarity problems, our results not only give new results but also extend/unify various similar results proved forC1, semismooth, and locally Lipschitzian.

scholarly journals MERIT FUNCTIONS FOR MATRIX CONE COMPLEMENTARITY PROBLEMS

2013 ◽  
Vol 31 (5_6) ◽  
pp. 795-812
Author(s):  
Li Wang ◽  
Yong-Jin Liu ◽  
Yong Jiang
Keyword(s):  
Complementarity Problems ◽  
Merit Functions

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.

Sign in / Sign up

Export Citation Format

Share Document