Parallel Newton methods for the nonlinear complementarity problem

In this paper, we discuss how the basic Newton method for solving the nonlinear complementarity problem can be implemented in a parallel computation environment. We propose some synchronized and asynchronous Newton methods and establish their convergence.

[1]  Dimitri P. Bertsekas,et al.  Distributed asynchronous computation of fixed points , 1983, Math. Program..

[2]  James M. Ortega,et al.  Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.

[3]  Lydia Kronsjö.  Computational complexity of sequential and parallel algorithms , 1986, Wiley series in computing.

[4]  J. Pang.  On the convergence of a basic iterative method for the implicit complementarity problem , 1982 .

[5]  Gérard M. Baudet,et al.  Asynchronous Iterative Methods for Multiprocessors , 1978, JACM.

[6]  Jong-Shi Pang,et al.  Inexact Newton methods for the nonlinear complementarity problem , 1986, Math. Program..

[7]  H. T. Kung,et al.  Synchronized and asynchronous parallel algorithms for multiprocessors , 1976 .

[8]  V. Shamanskii.  A modification of Newton's method , 1967 .

[9]  N. Josephy.  Newton's Method for Generalized Equations. , 1979 .

[10]  H. Mukai.  Parallel algorithms for solving systems of nonlinear equations , 1981 .

[11]  O. Mangasarian,et al.  Parallel successive overrelaxation methods for symmetric linear complementarity problems and linear programs , 1987 .

[12]  F. J. Gould,et al.  Homotopy methods and global convergence , 1983 .

[13]  J. Pang,et al.  Two-stage parallel iterative methods for the symmetric linear complementarity problem , 1988 .

[14]  J. Traub.  Iterative Methods for the Solution of Equations , 1982 .

[15]  Stephen M. Robinson,et al.  Strongly Regular Generalized Equations , 1980, Math. Oper. Res..

[16]  Jong-Shi Pang,et al.  Iterative methods for variational and complementarity problems , 1982, Math. Program..

[17]  N. Josephy.  Quasi-Newton methods for generalized equations , 1979 .

[18]  J. B. Rosen,et al.  A parallel algorithm for solving the linear complementarity problem , 1988 .

[19]  J. Pang.  Necessary and sufficient conditions for the convergence of iterative methods for the linear complementarity problem , 1984 .

[20]  B. Eaves.  Where Solving for Stationary Points by LCPs is Mixing Newton Iterates , 1983 .

[21]  O. Mangasarian,et al.  Parallel gradient projection successive overrelaxation for symmetric linear complementarity problems and linear programs , 1988 .