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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: Computational results show the robustness, efficiency, and high speed of the proposed algorithms for solving large scale Eigenvalue Complementarity Problems with real symmetric matrices.
Abstract: In this paper, we investigate a DC (Difference of Convex functions) programming technique for solving large scale Eigenvalue Complementarity Problems (EiCP) with real symmetric matrices. Three equivalent formulations of EiCP are considered. We first reformulate them as DC programs and then use DCA (DC Algorithm) for their solution. Computational results show the robustness, efficiency, and high speed of the proposed algorithms.
48 citations
Cites background from "Linear complementarity, linear and ..."
...In fact, finding α for a general strictly copositive matrix is a NP-hard problem [28]....
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TL;DR: In this paper, it was shown that the copositivity of a symmetric matrix of order n is equivalent to the coposiability of two symmetric matrices of order 1 if the matrix has a row whose off-diagonal elements are all nonpositive.
47 citations
TL;DR: In this article, a general accelerated modulus-based matrix splitting iteration method is established, which covers the known general modulusbased matrix-splitting iteration methods and the accelerated matrix splitting iterative methods.
Abstract: In this paper, a general accelerated modulus-based matrix splitting iteration method is established, which covers the known general modulus-based matrix splitting iteration methods and the accelerated modulus-based matrix splitting iteration methods. The convergence analysis is given when the system matrix is an $$H_+$$H+-matrix. Numerical examples show that the proposed methods are efficient and accelerate the convergence performance with less iteration steps and CPU times.
47 citations
TL;DR: Linear complementary problems (LCP) were considered in this article, where the authors fixed their notations and considered the solvability of linear complementarity problems with respect to the special properties of the coefficient matrix M.
46 citations
TL;DR: A general algorithm for checking regularity/singularity is presented which is not a priori exponential and based on a theoretical result according to which regularity may be judged from any single component of the solution set of an associated system of linear interval equations.
Abstract: Checking regularity (or singularity) of interval matrices is a known NP-hard problem. In this paper a general algorithm for checking regularity/singularity is presented which is not a priori exponential. The algorithm is based on a theoretical result according to which regularity may be judged from any single component of the solution set of an associated system of linear interval equations. Numerical experiments (with interval matrices up to the size n = 50) confirm that this approach brings an essential decrease in the amount of operations needed.
46 citations
Cites background from "Linear complementarity, linear and ..."
...has a unique solution x = (xi) for each right-hand side b if and only if A is a P -matrix (see Murty [11])....
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...The study of P -matrices is motivated, among other applications, by the fact that the linear complementarity problem x+ = Ax− + b has a unique solution x = (xi) for each right-hand side b if and only if A is a P -matrix (see Murty [11])....
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