Additive Schwarz algorithm for the nonlinear complementarity problem with M-function

2007 ◽  
Vol 190 (2) ◽  
pp. 1007-1019 ◽  
Author(s):  
Ying-Jun Jiang ◽  
Jin-Ping Zeng
Keyword(s):  
Complementarity Problem ◽  
Nonlinear Complementarity Problem ◽  
Nonlinear Complementarity ◽  
Additive Schwarz ◽  
Schwarz Algorithm

scholarly journals A MULTIPLICATIVE SCHWARZ ALGORITHM FOR THE NONLINEAR COMPLEMENTARITY PROBLEM WITH AN M-FUNCTION

2010 ◽  
Vol 82 (3) ◽  
pp. 353-366 ◽  
Author(s):  
YINGJUN JIANG ◽  
JINPING ZENG
Keyword(s):  
Complementarity Problem ◽  
Nonlinear Complementarity Problem ◽  
Iteration Algorithm ◽  
Monotone Convergence ◽  
Nonlinear Complementarity ◽  
Initial Values ◽  
Finite Dimensional ◽  
Regular Splitting ◽  
Norm Bound ◽  
Schwarz Algorithm

AbstractA multiplicative Schwarz iteration algorithm is presented for solving the finite-dimensional nonlinear complementarity problem with an M-function. The monotone convergence of the iteration algorithm is obtained with special choices of initial values. Moreover, by applying the concept of weak regular splitting, the weighted max-norm bound is derived for the iteration errors.

On an application of the complex nonlinear complementarity problem

1976 ◽  
Vol 15 (1) ◽  
pp. 141-148 ◽  
Author(s):  
J. Parida ◽  
B. Sahoo
Keyword(s):  
Minimization Problem ◽  
Complementarity Problem ◽  
Complex Space ◽  
Nonlinear Complementarity Problem ◽  
Polyhedral Cone ◽  
Convex Minimization ◽  
Convex Minimization Problem ◽  
Polyhedral Cones ◽  
Existence Of A Solution ◽  
Nonlinear Complementarity

A theorem on the existence of a solution under feasibility assumptions to a convex minimization problem over polyhedral cones in complex space is given by using the fact that the problem of solving a convex minimization program naturally leads to the consideration of the following nonlinear complementarity problem: given g: Cn → Cn, find z such that g(z) ∈ S*, z ∈ S, and Re〈g(z), z〉 = 0, where S is a polyhedral cone and S* its polar.

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