Properties of S-tensors

Guo, Qi; Zheng, Meng-Meng; Huang, Zheng-Hai

doi:10.1080/03081087.2018.1430737

Cited by 23 publications

(4 citation statements)

References 17 publications

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“…By using special properties of several classes of structured tensors [23], various properties of the solution set of the TCP(A , q) have been well studied, including the nonempty compactness of the solution set by Che, Qi and Wei [3], Song and Qi [25,26], Song and Yu [28], Gowda, Luo, Qi and Xiu [13], Luo, Qi and Xiu [20], and Wang, Huang and Bai [29]; the existence of solution by Huang, Suo and Wang [16], and Song and Qi [27]; the global uniqueness and solvability by Bai, Huang and Wang [1]; and the topological properties of the solution set and stability of the TCP(A , q) by Yu, Ling, He and Qi [30]. More recently, the strict feasibility of the TCP(A , q) was discussed with the help of S-tensor by Guo, Zheng and Huang [14]. In particular, Song and Qi [26] and Song and Yu [28] gave estimations of upper and lower bounds of the solution set of the TCP(A , q) with A being a P -tensor and a strictly semi-positive tensor, respectively.…”

Section: Mengmeng Zheng Ying Zhang and Zheng-hai Huangmentioning

confidence: 99%

Global error bounds for the tensor complementarity problem with a P-tensor

Zheng¹,

Zhang²,

Huang³

2019

Journal of Industrial &Amp; Management Optimization

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As a natural extension of the linear complementarity problem, the tensor complementarity problem has been studied recently; and many theoretical results have been obtained. In this paper, we investigate the global error bound for the tensor complementarity problem with a P-tensor. We give two global error bounds for this class of complementarity problems with the help of two positively homogeneous operators defined by a P-tensor. When the order of the involved tensor reduces to 2, the results obtained in this paper coincide exactly with the one for the linear complementarity problem. for some positive constants c 1 , c 2 , γ 1 and γ 2 , where r 1 and r 2 are two residual functions for the LCP (M, q), and dist(x, S) is the distance from the vector x to the set S. If T = R n , then (1) is called a global error bound for the LCP (M, q). The error bound has been studied extensively for the LCP (M, q).

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Section: Mengmeng Zheng Ying Zhang and Zheng-hai Huangmentioning

confidence: 99%

Global error bounds for the tensor complementarity problem with a P-tensor

Zheng¹,

Zhang²,

Huang³

2019

Journal of Industrial &Amp; Management Optimization

Self Cite

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“…In recent years, TCP has attracted much attention, and many theoretical results about the properties of the solution set of TCP have been developed, including existence of a unique solution [2,7,28,32,40], boundedness of solution sets [6,33,39], error bounds theory [18,41,44], the strictly feasibility [4,14], and so on. In addition, the properties of the solution map of TCP were investigated in [3,16] and an application of the TCP was given in [19].…”

Section: Introductionmentioning

confidence: 99%

Generalized Polynomial Complementarity Problems over a Polyhedral Cone

Shang

Yang

Tang

2021

J Optim Theory Appl

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The goal of this paper is to investigate a new model, called generalized polynomial complementarity problems over a polyhedral cone and denoted by GPCPs, which is a natural extension of the polynomial complementarity problems and generalized tensor complementarity problems. Firstly, the properties of the set of all R K 0 -tensors are investigated. Then, the nonemptiness and compactness of the solution set of GPCPs are proved, when the involved tensor in the leading term of the polynomial is an E R K -tensor. Subsequently, under fairly mild assumptions, lower bounds of solution set via an equivalent form are obtained. Finally, a local error bound of the considered problem is derived. The results presented in this paper generalize and improve the corresponding those in the recent literature. Keywords Generalized polynomial complementarity problemCommunicated by Alexey F. Izmailov.

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“…As a natural extension of the linear complementarity problem, the TCP( , A) emerged from the tensor community in 2015 [1]. In recent several years, the TCP( , A) has been a hot topic and many theoretical results have been obtained, including the nonemptiness and/or compactness of solution set [4][5][6][7][8][9][10][11][12][13][14][15][16], the existence of unique solution [7,8,14,[17][18][19][20][21][22], error bound theory [23][24][25], strict feasibility [22,26], and so on. Several algorithms for solving the TCP( , A) have also been proposed [27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Solvability of Two Classes of Tensor Complementarity Problems

Yang

2019

Mathematical Problems in Engineering

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In this paper, we first introduce a class of tensors, called positive semidefinite plus tensors on a closed cone, and discuss its simple properties; and then, we focus on investigating properties of solution sets of two classes of tensor complementarity problems. We study the solvability of a generalized tensor complementarity problem with aD-strictly copositive tensor and a positive semidefinite plus tensor on a closed cone and show that the solution set of such a complementarity problem is bounded. Moreover, we prove that a related conic tensor complementarity problem is solvable if the involved tensor is positive semidefinite on a closed convex cone and is uniquely solvable if the involved tensor is strictly positive semidefinite on a closed convex cone. As an application, we also investigate a static traffic equilibrium problem which is reformulated as a concerned complementarity problem. A specific example is also given.

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Properties of S-tensors

Cited by 23 publications

References 17 publications

Global error bounds for the tensor complementarity problem with a <i>P</i>-tensor

Global error bounds for the tensor complementarity problem with a <i>P</i>-tensor

Generalized Polynomial Complementarity Problems over a Polyhedral Cone

Solvability of Two Classes of Tensor Complementarity Problems

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