Open AccessJournal Article
Variational Inequality Formulation of the Asymmetric Eigenvalue Complementarity Problem and its Solution By Means of Gap Functions
TLDR
In this article, a hybrid algorithm combining a projection technique and a modified Josephy-Newton method is proposed to solve the asymmetric eigenvalue comple- mentarity problem by finding a stationary point of the gap function and the regularized gap function.Abstract:
In this paper, the solution of the asymmetric eigenvalue comple- mentarity problem (EiCP) is investigated by means of a variational inequality formulation. This problem is then solved by finding a stationary point of the gap function and the regularized gap function. A nonlinear programming formulation of the EiCP results from the gap function. A hybrid algorithm combining a projection technique and a modified Josephy-Newton method is proposed to solve the EiCP by finding a stationary point of the regularized gap function. Numerical results show that the proposed method can in gen- eral solve EiCPs efficiently.read more
Citations
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Journal ArticleDOI
On the computation of all eigenvalues for the eigenvalue complementarity problem
TL;DR: A parametric algorithm is introduced for computing all eigenvalues for two Eigenvalue Complementarity Problems discussed in the literature and a hybrid method that combines an enumerative method and a semi-smooth algorithm is discussed.
Journal ArticleDOI
Complementary eigenvalues of graphs
TL;DR: In this article, the authors studied the Eigenvalue Complementarity Problem (EiCP) when the adjacency matrix of a connected graph has a unique complementary eigenvalue.
Journal ArticleDOI
On an enumerative algorithm for solving eigenvalue complementarity problems
TL;DR: An extension of the enumerative algorithm for the quadratic EiCP is developed, which solves this problem by computing a global minimum for the NLP formulation, and some computational experience is presented to highlight the efficiency and efficacy of the proposed enumerative algorithms.
Journal ArticleDOI
A block active set algorithm with spectral choice line search for the symmetric eigenvalue complementarity problem
TL;DR: This paper addresses the solution of the symmetric eigenvalue complementarity problem (EiCP) by treating an equivalent reformulation of finding a stationary point of a fractional quadratic program on the unit simplex by the spectral projected-gradient method.
Journal ArticleDOI
On the quadratic eigenvalue complementarity problem
TL;DR: A new sufficient condition for existence of solutions of this problem is established, which is somewhat more manageable than previously existent ones, and the introduction of auxiliary variables leads to the reduction of QEiCP to an Eigenvalue Complementarity Problem in higher dimension.
References
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Book
Finite-Dimensional Variational Inequalities and Complementarity Problems
TL;DR: Newton Methods for Nonsmooth Equations as mentioned in this paper and global methods for nonsmooth equations were used to solve the Complementarity problem in the context of non-complementarity problems.
Book
The Linear Complementarity Problem
TL;DR: In this article, the authors present an overview of existing and multiplicity of degree theory and propose pivoting methods and iterative methods for degree analysis, including sensitivity and stability analysis.
Journal ArticleDOI
Nonmonotone Spectral Projected Gradient Methods on Convex Sets
TL;DR: The classical projected gradient schemes are extended to include a nonmonotone steplength strategy that is based on the Grippo--Lampariello--Lucidi non monotone line search that is combined with the spectral gradient choice of steplENGTH to accelerate the convergence process.