A new logarithmic-quadratic proximal method for nonlinear complementarity problems

2009 ◽  
Vol 215 (2) ◽  
pp. 695-706 ◽  
Author(s):  
Abdellah Bnouhachem ◽  
Muhammad Aslam Noor ◽  
Mohamed Khalfaoui ◽  
Sheng Zhaohan
Keyword(s):  
Complementarity Problems ◽  
Nonlinear Complementarity Problems ◽  
Proximal Method ◽  
Nonlinear Complementarity

A New Hybrid Inexact Logarithmic-Quadratic Proximal Method for Nonlinear Complementarity Problems

2012 ◽  
pp. 158-168
Author(s):  
Ying Zhou ◽  
Lizhi Wang
Keyword(s):  
Numerical Experiments ◽  
Proximal Point Algorithm ◽  
Complementarity Problems ◽  
Nonlinear Complementarity Problems ◽  
New Method ◽  
Proximal Method ◽  
Proximal Point ◽  
Nonlinear Complementarity ◽  
Correction Step

In this paper, the authors present and analyze a new hybrid inexact Logarithmic-Quadratic Proximal method for solving nonlinear complementarity problems. Each iteration of the new method consists of a prediction and a correction step. The predictor is produced using an inexact Logarithmic-Quadratic Proximal method, which is then corrected by the Proximal Point Algorithm. The new iterate is obtained by combining predictor and correction point at each iteration. In this paper, the authors prove the convergence of the new method under the mild assumptions that the function involved is continuous and monotone. Comparison to another existing method with numerical experiments on classical NCP instances demonstrates its superiority.

A New Hybrid Inexact Logarithmic-Quadratic Proximal Method for Nonlinear Complementarity Problems

2010 ◽  
Vol 1 (3) ◽  
pp. 1-13
Author(s):  
Ying Zhou ◽  
Lizhi Wang
Keyword(s):  
Numerical Experiments ◽  
Proximal Point Algorithm ◽  
Complementarity Problems ◽  
Nonlinear Complementarity Problems ◽  
New Method ◽  
Proximal Method ◽  
Proximal Point ◽  
Nonlinear Complementarity ◽  
Correction Step

In this paper, the authors present and analyze a new hybrid inexact Logarithmic-Quadratic Proximal method for solving nonlinear complementarity problems. Each iteration of the new method consists of a prediction and a correction step. The predictor is produced using an inexact Logarithmic-Quadratic Proximal method, which is then corrected by the Proximal Point Algorithm. The new iterate is obtained by combining predictor and correction point at each iteration. In this paper, the authors prove the convergence of the new method under the mild assumptions that the function involved is continuous and monotone. Comparison to another existing method with numerical experiments on classical NCP instances demonstrates its superiority.

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