The solution of the linear complementarity problem by the matrix analogue of the accelerated overrelaxation iterative method

2016 ◽  
Vol 73 (3) ◽  
pp. 665-684 ◽  
Author(s):  
Apostolos Hadjidimos ◽  
Michael Tzoumas
Keyword(s):  
Iterative Method ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Linear Complementarity ◽  
The Matrix ◽  
Overrelaxation Iterative Method

An Iterative Approach to Dynamic Elastic-Plastic Analysis

1998 ◽  
Vol 65 (4) ◽  
pp. 811-819 ◽  
Author(s):  
F. Giambanco ◽  
L. Palizzolo ◽  
L. Cirone
Keyword(s):  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Degrees Of Freedom ◽  
Linear Complementarity ◽  
Iterative Approach ◽  
Loading History ◽  
Constraint Matrix ◽  
Elastic Plastic ◽  
Recursive Solution ◽  
The Matrix

The step-by-step analysis of structures constituted by elastic-plastic finite elements, subjected to an assigned loading history, is here considered. The structure may possess dynamic and/or not dynamic degrees-of-freedom. As it is well-known, at each step of analysis the solution of a linear complementarity problem is required. An iterative method devoted to solving the relevant linear complementarity problem is presented. It is based on the recursive solution of a linear complementarity, problem in which the constraint matrix is block-diagonal and deduced from the matrix of the original linear complementarity problem. The convergence of the procedure is also proved. Some particular cases are examined. Several numerical applications conclude the paper.

scholarly journals A linear complementarity problem involving a subgradient

1988 ◽  
Vol 37 (3) ◽  
pp. 345-351 ◽  
Author(s):  
J. Parida ◽  
A. Sen ◽  
A. Kumar
Keyword(s):  
Convex Function ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Nonlinear Complementarity Problem ◽  
Linear Complementarity ◽  
Existence Of A Solution ◽  
Nonlinear Complementarity ◽  
The Matrix ◽  
Square Matrix

A linear complementarity problem, involving a given square matrix and vector, is generalised by including an element of the subdifferential of a convex function. The existence of a solution to this nonlinear complementarity problem is shown, under various conditions on the matrix. An application to convex nonlinear nondifferentiable programs is presented.

A Preconditioned Gauss-Seidel Iterative Method for Linear Complementarity Problem in Intelligent Materials System

2011 ◽  
Vol 340 ◽  
pp. 3-8 ◽  
Author(s):  
Ban Xiang Duan ◽  
Wen Ying Zeng ◽  
Xiao Ping Zhu
Keyword(s):  
Iterative Method ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Sufficient Conditions ◽  
Linear Complementarity ◽  
Computational Results ◽  
System Matrix ◽  
Intelligent Materials ◽  
Preconditioned Matrix ◽  
Set Up

In this paper, the authors first set up new preconditioned Gauss-Seidel iterative method for solving the linear complementarity problem, whose preconditioned matrix is introduced. Then certain elementary operations row are performed on system matrix before applying the Gauss-Seidel iterative method. Moreover the sufficient conditions for guaranteeing the convergence of the new preconditioned Gauss-Seidel iterative method are presented. Lastly we report some computational results with the proposed method.

Sign in / Sign up

Export Citation Format

Share Document