scholarly journals Convergence Analysis of a Trust-Region Multidimensional Filter Method for Nonlinear Complementarity Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
C. W. Wu ◽  
J. P. Cao ◽  
L. F. Wang
Keyword(s):  
Quadratic Programming ◽  
Convergence Analysis ◽  
Numerical Experiments ◽  
Complementarity Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Nonlinear Complementarity Problems ◽  
Filter Method ◽  
Nonlinear Complementarity ◽  
Globally Convergent

For solving nonlinear complementarity problems, a new algorithm is proposed by using multidimensional filter techniques and a trust-region method. The algorithm is shown to be globally convergent under the reasonable assumptions and does not depend on any extra restoration procedure. In particular, it shows that the subproblem is a convex quadratic programming problem, which is easier to be solved. The results of numerical experiments show its efficiency.

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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