Remarks on Convergence of the Matrix Splitting Algorithm for the Symmetric Linear Complementarity Problem

1993 ◽  
Vol 3 (1) ◽  
pp. 155-163 ◽  
Author(s):  
Wu Li
Keyword(s):  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Linear Complementarity ◽  
Matrix Splitting ◽  
Splitting Algorithm ◽  
The Matrix

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.

scholarly journals Two-step modulus-based matrix splitting iteration method for horizontal linear complementarity problems

Filomat ◽  
2020 ◽  
Vol 34 (7) ◽  
pp. 2171-2184
Author(s):  
Lu Jia ◽  
Xiang Wang ◽  
Xuan-Sheng Wang
Keyword(s):  
Theoretical Analysis ◽  
Linear Complementarity Problem ◽  
Iteration Method ◽  
Complementarity Problem ◽  
Numerical Experiments ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Matrix Splitting ◽  
Splitting Iteration Method

The modulus-based matrix splitting iteration has received substantial attention as a momentous tool for complementarity problems. For the purpose of solving the horizontal linear complementarity problem, we introduce the two-step modulus-based matrix splitting iteration method. We also show the theoretical analysis of the convergence. Numerical experiments illustrate the effectiveness of the proposed approach.

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