A positive interior-point algorithm for nonlinear complementarity problems

2003 ◽  
Vol 24 (3) ◽  
pp. 355-362 ◽  
Author(s):  
Ma Chang-feng ◽  
Liang Guo-ping ◽  
Chen Xin-mei
Keyword(s):  
Interior Point ◽  
Complementarity Problems ◽  
Nonlinear Complementarity Problems ◽  
Interior Point Algorithm ◽  
Nonlinear Complementarity

scholarly journals Long step homogeneous interior point algorithm for the p* nonlinear complementarity problems

2002 ◽  
Vol 12 (1) ◽  
pp. 17-48
Author(s):  
Goran Lesaja
Keyword(s):  
Global Convergence ◽  
Linear Complementarity Problem ◽  
Interior Point ◽  
Complementarity Problem ◽  
Complementarity Problems ◽  
Nonlinear Complementarity Problem ◽  
Linear Complementarity ◽  
Compact Set ◽  
Interior Point Algorithm ◽  
Nonlinear Complementarity

A P*-Nonlinear Complementarity Problem as a generalization of the P*-Linear Complementarity Problem is considered. We show that the long-step version of the homogeneous self-dual interior-point algorithm could be used to solve such a problem. The algorithm achieves linear global convergence and quadratic local convergence under the following assumptions: the function satisfies a modified scaled Lipschitz condition, the problem has a strictly complementary solution, and certain submatrix of the Jacobian is nonsingular on some compact set.

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