Splitting methods for the Eigenvalue Complementarity Problem

Iusem, Alfredo N.; Júdice, Joaquim J.; Sessa, Valentina; Sarabando, Paula

doi:10.1080/10556788.2018.1479408

Cited by 10 publications

(2 citation statements)

References 21 publications

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“…Como ocurre con los vectores propios convencionales, los vectores propios complementarios asociados a un valor propio complementario también forman un conjunto infinito, el cual es un cono convexo (Iusem, J údice, Sessa, y Sarabando, 2019). Esto puede verse fácilmente con las siguientes matrices, A = 18 0 0 1 y B = 9 3 3 5 .…”

Section: Introductionunclassified

Resolviendo el problema de valores propios complementarios mediante un algoritmo cuasi-Newton

Arenas¹,

Arias²,

Perez³

2022

Rev. Acad. Colomb. Cienc. Ex. Fis. Nat.

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En este artículo consideramos el problema de valores propios complementarios, de gran interés para muchos investigadores por sus numerosas aplicaciones en Ingeniería y Física, y abordamos su solución como un problema de complementariedad no lineal usando un método cuasi-Newton, un tipo de método que, hasta donde conocemos, no ha sido utilizado para dicho fin. Verificamos que el problema satisface ciertas hipótesis que permiten utilizar un algoritmo global cuasi-Newton y realizamos pruebas numéricas que muestran la eficacia del algoritmo utilizado y lo hacen una buena alternativa de solución para problemas de valores propios complementarios.

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Section: Introductionunclassified

Resolviendo el problema de valores propios complementarios mediante un algoritmo cuasi-Newton

Arenas¹,

Arias²,

Perez³

2022

Rev. Acad. Colomb. Cienc. Ex. Fis. Nat.

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“…During the past several years, many theoretical results [2,3,4,5], applications [6,7,8] and extensions [9,10,11,12,13,14] of EiCP have been discussed and a number of efficient algorithms have been proposed for the solution of this problem [15,16,17,18,19,20,21,22]. Contrary to the EiCP, QEiCP may have no solution even when the matrix A of the leading λ-term is PD [23].…”

Section: Introductionmentioning

confidence: 99%

Improved dc programming approaches for solving the quadratic eigenvalue complementarity problem

Niu

Júdice

Thi

et al. 2019

Applied Mathematics and Computation

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In this paper, we discuss the solution of a Quadratic Eigenvalue Complementarity Problem (QEiCP) by using Difference of Convex (DC) programming approaches. We first show that QEiCP can be represented as dc programming problem. Then we investigate different dc programming formulations of QEiCP and discuss their dc algorithms based on a well-known method -DCA. A new local dc decomposition is proposed which aims at constructing a better dc decomposition regarding to the specific feature of the target problem in some neighborhoods of the iterates. This new procedure yields faster convergence and better precision of the computed solution. Numerical results illustrate the efficiency of the new dc algorithms in practice.

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An active-set algorithmic framework for non-convex optimization problems over the simplex

et al. 2020

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Splitting methods for the Eigenvalue Complementarity Problem

Cited by 10 publications

References 21 publications

Resolviendo el problema de valores propios complementarios mediante un algoritmo cuasi-Newton

Resolviendo el problema de valores propios complementarios mediante un algoritmo cuasi-Newton

Improved dc programming approaches for solving the quadratic eigenvalue complementarity problem

An active-set algorithmic framework for non-convex optimization problems over the simplex

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