On the Quadratic Eigenvalue Complementarity Problem over a general convex cone

Brás, Carmo P.; Fukushima, Masao; Iusem, Alfredo N.; Júdice, Joaquim J.

doi:10.1016/j.amc.2015.09.014

Cited by 4 publications

(2 citation statements)

References 30 publications

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“…A number of algorithms have been proposed for the solution of QEiCP and its extensions to other cases when A ∈ PD and one of the conditions C / ∈ S 0 or co-hyperbolicity holds [15,25,23,26,18,27,28,1]. Two nonlinear programming (NLP) formulations of QEiCP have been introduced in [23,18] such that (λ, x) is a solution of QEiCP if and only if (λ, x) is a global minimum of NLP with an optimal value equal to zero.…”

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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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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“…For getting acquainted with the theory of cone-constrained affine eigenvalue problems the reader may consult Seeger [17], Seeger and Torki [19], Pinto da Costa and Seeger [14,15], and references therein. Coneconstrained quadratic eigenvalue problems are considered in Seeger [18], Brás et al [4,5], Fernandes et al [7], Iusem et al [9,10], and Niu et al [13].…”

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confidence: 99%

Cone-constrained rational eigenvalue problems

Seeger

2019

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This work deals with the eigenvalue analysis of a rational matrix-valued function subject to complementarity constraints induced by a polyhedral cone $K$. The eigenvalue problem under consideration has the general structure \[ \left(\sum_{k=0}^d \lambda^k A_k + \sum_{k =1}^m \frac{p_k(\lambda)}{q_k(\lambda)} \,B_k\right) x = y , \quad K\ni x \perp y\in K^\ast, \] where $K^\ast$ denotes the dual cone of $K$. The unconstrained version of this problem has been discussed in [Y.F. Su and Z.J. Bai. Solving rational eigenvalue problems via linearization. \emph{SIAM J. Matrix Anal. Appl.}, 32:201--216, 2011.] with special emphasis on the implementation of linearization-based methods. The cone-constrained case can be handled by combining Su and Bai's linearization approach and the so-called facial reduction technique. In essence, this technique consists in solving one unconstrained rational eigenvalue problem for each face of the polyhedral cone $K$.

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