On eigenvalues induced by a cone constraint

Seeger, Alberto; Torki, Mounir

doi:10.1016/s0024-3795(03)00553-6

Cited by 54 publications

(37 citation statements)

References 7 publications

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“…if A is symmetric, then When m = 2, both λ(A) and µ(A) are the smallest Pareto eigenvalue of a matrix A, denote by λ(A). For more details on Pareto eigenvalue of a matrix, see Seeger [40], Seeger, Torki [41] and Hiriart-Urruty, Seeger [42]. Then the following conclusions are easy to obtain.…”

Section: Boundedness Of Solution Set Of Tcp(a Q)mentioning

confidence: 89%

Strictly semi-positive tensors and the boundedness of tensor complementarity problems

Song

2016

Optim Lett

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In this paper, we present the boundedness of solution set of tensor complementarity problem defined by a strictly semi-positive tensor. For strictly semi-positive tensor, we prove that all H + (Z + )-eigenvalues of each principal sub-tensor are positive. We define two new constants associated with H + (Z + )-eigenvalues of a strictly semi-positive tensor. With the help of these two constants, we establish upper bounds of an important quantity whose positivity is a necessary and sufficient condition for a general tensor to be a strictly semi-positive tensor. The monotonicity and boundedness of such a quantity are established too.

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Section: Boundedness Of Solution Set Of Tcp(a Q)mentioning

confidence: 89%

Strictly semi-positive tensors and the boundedness of tensor complementarity problems

Song

2016

Optim Lett

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“…For the general theory behind Problems 1 and 2, the reader is conveyed to the references [7,11,15,16]. This note focuses only on numerical issues.…”

Section: Problemmentioning

confidence: 99%

“…As shown in [16], the set σ θ ( A) could perfectly well contain one or more intervals of positive length. As seen in Figure 1, the dual cone of L θ is again a circular cone.…”

Section: Problemmentioning

confidence: 99%

Numerical resolution of cone-constrained eigenvalue problems

Costa¹,

Seeger²

2009

Comput.appl.math.

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Abstract. Given a convex cone K and matrices A and B, one wishes to find a scalar λ and a nonzero vector x satisfying the complementarity systemThis problem arises in mechanics and in other areas of applied mathematics. Two numerical techniques for solving such kind of cone-constrained eigenvalue problem are discussed, namely, the Power Iteration Method and the Scaling and Projection Algorithm.Mathematical subject classification: 65F15, 90C33.

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“…Proof Combine [10,Theorem 3.3] and [18,Theorem 2.5] for the existential part. The compactness result is obvious.…”

Section: Proposition 1 Under (2) the Set σ K (A B) Is Nonempty And Cmentioning

confidence: 99%

Cone-constrained eigenvalue problems: theory and algorithms

Costa

Seeger

2008

Comput Optim Appl

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On eigenvalues induced by a cone constraint

Cited by 54 publications

References 7 publications

Strictly semi-positive tensors and the boundedness of tensor complementarity problems

Strictly semi-positive tensors and the boundedness of tensor complementarity problems

Numerical resolution of cone-constrained eigenvalue problems

Cone-constrained eigenvalue problems: theory and algorithms

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