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Linear complementarity, linear and nonlinear programming
01 Jan 1988-
About: The article was published on 1988-01-01 and is currently open access. It has received 1012 citations till now. The article focuses on the topics: Mixed complementarity problem & Complementarity theory.
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TL;DR: In this paper, error bounds for linear complementarity problems are obtained when the involved matrices are weakly chained diagonally dominant B-matrices and numerical examples are given to show the effectiveness of the proposed bounds.
Abstract: Abstract Some new error bounds for the linear complementarity problems are obtained when the involved matrices are weakly chained diagonally dominant B-matrices. Numerical examples are given to show the effectiveness of the proposed bounds.
6 citations
Journal Article•
TL;DR: In this article, the projected dynamical system associated with absolute value variational inequalities is analyzed using the projection method, and different iterative algorithms for solving the variational inequality by discretizing the corresponding projected dynamic system are proposed.
Abstract: In this paper, we consider the absolute value variational inequalities We propose and analyze the projected dynamical system associated with absolute value variational inequalities by using the projection method We suggest different iterative algorithms for solving absolute value variational inequalities by discretizing the corresponding projected dynamical system The convergence of the suggested methods is proved under suitable constraints Numerical examples are given to illustrate the efficiency and implementation of the methods Results proved in this paper continue to hold for previously known classes of absolute value variational inequalities
6 citations
Cites methods from "Linear complementarity, linear and ..."
...Since the discovery of variational inequalities theory, a number of numerical methods including projection method, Wiener-Hopf equations, auxiliary principle and dynamical systems has been developed for solving the variational inequalities and the related optimization problems, see the references therein [1-49]....
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...The equivalence between variational inequalities and complementarity problem has been used in suggesting many iterative algorithms for solving complementarity problems, see [17,26,27,37]....
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01 Jan 2013
TL;DR: This paper provides the efficient iterative algorithm for the large sparse Non-Hermitian positive definite systems of LCP, based on the splitting of the coefficient matrix and fixed-point principle.
Abstract: Many problems in various scientific computing, operations research, management science and engineering areas can lead to the solution of a linear complementarity problem (LCP ). This paper provides the efficient iterative algorithm for the large sparse Non-Hermitian positive definite systems of LCP , based on the splitting of the coefficient matrix and fixed-point principle. Also, the global convergence properties of the proposed method have been analyzed. Numerical results show the applicability of our method.
6 citations
TL;DR: Based on the optimization algorithms used for multi-body dynamics with unilateral contacts, an algorithm by means of artificial neural network (NNW) is developed in this article, where the cable-structures are considered as a class of mechanical complementary slackness systems.
Abstract: In the present paper, the cable-structures are considered as a class of mechanical complementary-slackness systems. Based on the optimization algorithms used for multi-body dynamics with unilateral contacts, an algorithm by means of artificial neural network (NNW) is developed. The following two classes of cable-structures have been considered force-elongation of cable member follows elastic behavior and work-hardening assumption. Due to simplicity the former is used to prove the method reliability, and the latter, as general cable-structure problem is handled. First, the complementarity problems for those structures have been formulated; then using generalized Gaussian‘ least action principle they are summarized as an optimization problem. Based on Hopfield’s work, an artificial NNW has been designed and used to decide combination of possible constraints at each step in simulation. As examples, two cable-structures have been investigated. The calculated results for a simple suspension structure evidence the reliability and time-economization of the proposed method. An example of guyed mast shows the suitability of the proposed method for practical cable-structures.
6 citations
Cites background from "Linear complementarity, linear and ..."
...In spite of many value contributions to the numerics of non-continuous systems [14] the existing algorithms are still extremely time-consuming....
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TL;DR: In this article, a mixed finite element and mesh-free method for gradient-dependent plasticity using linear complementarity theory is presented, where the assumed displacement field is interpolated in terms of its discrete values defined at the nodal points of the FE mesh with the FE shape functions.
Abstract: A mixed finite element (FE) and mesh-free (MF) method for gradient-dependent plasticity using linear complementarity theory is presented. The assumed displacement field is interpolated in terms of its discrete values defined at the nodal points of the FE mesh with the FE shape functions, whereas the assumed plastic multiplier field required to express its Laplacian is interpolated in terms of its discrete values defined at the integration points of the FE mesh with the MF interpolation functions. A standard form of linear complementarity problem is constructed by combining the weak form of momentum conservation equation and pointwise enforcements of both non-local constitutive equation and non-local yield criterion. The discrete values of the plastic multiplier are taken as the only primary unknowns to be determined. The numerical results demonstrate the validity of the proposed method in the simulation of the strain localization phenomenon due to strain softening.
6 citations