A Semismooth Newton Method for Tensor Eigenvalue Complementarity Problem

Chen, Zhongming; Qi, Liqun

doi:10.48550/arxiv.1510.08570

Cited by 2 publications

(5 citation statements)

References 32 publications

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“…Since inf α k = 0, there exists a subsequence {x k } K such that lim k∈K α k = 0. In such a case, from the way α k is chosen in (8), there exists an index k sufficiently large such that for all k ≥ k, k ∈ K, for which α k /0.5 fails to satisfy condition (8), i.e., f…”

Section: Algorithm 1: Spectral Projected Gradient (Spg1) Algorithm Fo...mentioning

confidence: 99%

“…The properties of Pareto eigenvalues and their connection to polynomial optimization are studied in [37]. Recently, as a special type of nonlinear complementarity problems, the tensor complementarity problem is inspiring more and more research in the literature [2,6,8,9,13,15,26,38,39,40]. A shifted projected power method for TEiCP was proposed in [9], in which they need an adaptive shift to force the objective to be (locally) convex to guarantee the convergence of power method.…”

Section: Introductionmentioning

confidence: 99%

“…One main shortcoming of SPA is the stepsize will approach to zero as the sequence gets close to a solution of TEiCP [24]. Recently, by introducing an NCP-function, Chen and Qi [8] reformulated the TEiCP as a system of nonlinear equations. And then, they proposed a semismooth Newton method for solving the system of nonlinear equations [8].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, by introducing an NCP-function, Chen and Qi [8] reformulated the TEiCP as a system of nonlinear equations. And then, they proposed a semismooth Newton method for solving the system of nonlinear equations [8].…”

Section: Introductionmentioning

confidence: 99%

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Spectral projected gradient methods for generalized tensor eigenvalue complementarity problems

Song

et al. 2018

Numer Algor

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This paper looks at the tensor eigenvalue complementarity problem (TEiCP) which arises from the stability analysis of finite dimensional mechanical systems and is closely related to the optimality conditions for polynomial optimization. We investigate two monotone ascent spectral projected gradient (SPG) methods for TEiCP. We also present a shifted scaling-and-projection algorithm (SPA), which is a great improvement of the original SPA method proposed by Ling, He and Qi [Comput. Optim. Appl., DOI 10.1007/s10589-015-9767-z]. Numerical comparisons with some existed gradient methods in the literature are reported to illustrate the efficiency of the proposed methods.

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Section: Algorithm 1: Spectral Projected Gradient (Spg1) Algorithm Fo...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Spectral projected gradient methods for generalized tensor eigenvalue complementarity problems

Song

et al. 2018

Numer Algor

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“…When the tensors are symmetric, they reformulated the problem as nonlinear optimization and then proposed a shifted projected power method. Chen and Qi [4] reformulated the TEiCP as a system of nonlinear equations and proposed a damped semi-smooth Newton method for solving it. Some properties of Pareto-eigenvalues are further studied in [42].…”

Section: Introductionmentioning

confidence: 99%

Tensor Eigenvalue Complementarity Problems

Fan

Nie

Zhou

2016

Preprint

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This paper studies tensor eigenvalue complementarity problems. Basic properties of standard and complementarity tensor eigenvalues are discussed. We formulate tensor eigenvalue complementarity problems as constrained polynomial optimization. When one tensor is strictly copositive, the complementarity eigenvalues can be computed by solving polynomial optimization with normalization by strict copositivity. When no tensor is strictly copositive, we formulate the tensor eigenvalue complementarity problem equivalently as polynomial optimization by a randomization process. The complementarity eigenvalues can be computed sequentially. The formulated polynomial optimization can be solved by Lasserre's hierarchy of semidefinite relaxations. We show that it has finite convergence for generic tensors. Numerical experiments are presented to show the efficiency of proposed methods.

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A Semismooth Newton Method for Tensor Eigenvalue Complementarity Problem

Cited by 2 publications

References 32 publications

Spectral projected gradient methods for generalized tensor eigenvalue complementarity problems

Spectral projected gradient methods for generalized tensor eigenvalue complementarity problems

Tensor Eigenvalue Complementarity Problems

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