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Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalitiesMath. Comput., 67
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A Survey of Some Nonsmooth Equations and Smoothing Newton Methods
J. Burke, Song Xu (1998)
The Global Linear Convergence of a Noninterior Path-Following Algorithm for Linear Complementarity ProblemsMath. Oper. Res., 23
C. Kanzow (1996)
Some Noninterior Continuation Methods for Linear Complementarity ProblemsSIAM J. Matrix Anal. Appl., 17
S. Engelke (2000)
Hamburger Beitrage zur Angewandten Mathematik Improved Smoothing-Type Methods for the Solution of Linear Programs
B. Chen, N. Xiu (2001)
Superlinear Noninterior One-Step Continuation Method for Monotone LCP in the Absence of Strict ComplementarityJournal of Optimization Theory and Applications, 108
Chunhui Chen, O. Mangasarian (1995)
Smoothing methods for convex inequalities and linear complementarity problemsMathematical Programming, 71
Bintong Chen, Xiaojun Chen (1999)
A Global and Local Superlinear Continuation-Smoothing Method for P0 and R0 NCP or Monotone NCPSIAM J. Optim., 9
Xiaojun Chen, Y. Ye (1999)
On Homotopy-Smoothing Methods for Variational InequalitiesSiam Journal on Control and Optimization
J. Burke, Song Xu (1998)
A Non-Interior Predictor-Corrector Path-Following Method for LCP
P. Tseng (1998)
Analysis Of A Non-Interior Continuation Method Based On Chen-Mangasarian Smoothing Functions For Com
Bintong Chen, N. Xiu (1999)
A Global Linear and Local Quadratic Noninterior Continuation Method for Nonlinear Complementarity Problems Based on Chen-Mangasarian Smoothing FunctionsSIAM J. Optim., 9
S. Robinson (1981)
Some continuity properties of polyhedral multifunctions
Keisuke Hotta, Akiko Yoshise (1999)
Global convergence of a class of non-interior point algorithms using Chen-Harker-Kanzow-Smale functions for nonlinear complementarity problemsMathematical Programming, 86
L. Qi, Jie Sun (1993)
A nonsmooth version of Newton's methodMathematical Programming, 58
Bintong Chen, P. Harker (1993)
A Non-Interior-Point Continuation Method for Linear Complementarity ProblemsSIAM J. Matrix Anal. Appl., 14
Xiaojun Chen, Y. Ye (1999)
On Homotopy-Smoothing Methods for Box-Constrained Variational InequalitiesSiam Journal on Control and Optimization, 37
J. Burke, Song Xu (2000)
A non–interior predictor–corrector path following algorithm for the monotone linear complementarity problemMathematical Programming, 87
L. Qi, Defeng Sun (2002)
Smoothing Functions and Smoothing Newton Method for Complementarity and Variational Inequality ProblemsJournal of Optimization Theory and Applications, 113
In this paper, we analyze the global and local convergence properties of two predictor-corrector smoothing methods, which are based on the framework of the method in [1], for monotone linear complementarity problems (LCPs). The difference between the algorithm in [1] and our algorithms is that the neighborhood of smoothing central path in our paper is different to that in [1]. In addition, the difference between Algorithm 2.1 and the algorithm in [1] exists in the calculation of the predictor step. Comparing with the results in [1], the global and local convergence of the two methods can be obtained under very mild conditions. The global convergence of the two methods do not need the boundness of the inverse of the Jacobian. The superlinear convergence of Algorithm 2.1′ is obtained under the assumption of nonsingularity of generalized Jacobian of φ(x, y) at the limit point and Algorithm 2.1 obtains superlinear convergence under the assumption of strict complementarity at the solution. The effciency of the two methods is tested by numerical experiments.
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Jan 1, 2004
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