Local Uniqueness of Solutions to the Extended Linear Complementarity Problem

1999 ◽  
Vol 103 (3) ◽  
pp. 715-726 ◽  
Author(s):  
J. Z. Zhang ◽  
N. H. Xiu
Keyword(s):  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Linear Complementarity ◽  
Local Uniqueness ◽  
Uniqueness Of Solutions ◽  
Extended Linear Complementarity Problem ◽  
Local Uniqueness Of Solutions

A globally convergent damped Gauss–Newton method for solving the extended linear complementarity problem

2015 ◽  
Vol 23 (3) ◽  
Author(s):  
Na Huang ◽  
Changfeng Ma
Keyword(s):  
Newton Method ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Complementarity Problems ◽  
Optimization Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
System Of Equations ◽  
Extended Linear Complementarity Problem ◽  
Special Cases

AbstractThe extended linear complementarity problem (denoted by XLCP), of which the linear and horizontal linear complementarity problems are two special cases, can be reformulated as the solution of a nonsmooth system of equations. By the symmetrically perturbed smoothing Fischer-Burmeister function, the XLCP is approximated by a family of parameterized smoothness optimization problems. Asmoothing damped Gauss-Newton method is designed for solving the XLCP. The proposed algorithm is proved to be convergent globally under suitable assumptions. Some numerical results are reported in the paper

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