Tensor Complementarity Problem and Semi-positive Tensors

Yisheng Song; Liqun Qi

doi:10.1007/s10957-015-0800-2

Tensor Complementarity Problem and Semi-positive Tensors

Yisheng Song, Liqun Qi

Research output: Journal article publication › Journal article › Academic research › peer-review

94 Citations (Scopus)

Abstract

In this paper, we prove that a real tensor is strictly semi-positive if and only if the corresponding tensor complementarity problem has a unique solution for any nonnegative vector and that a real tensor is semi-positive if and only if the corresponding tensor complementarity problem has a unique solution for any positive vector. It is shown that a real symmetric tensor is a (strictly) semi-positive tensor if and only if it is (strictly) copositive.

Original language	English
Pages (from-to)	1069-1078
Number of pages	10
Journal	Journal of Optimization Theory and Applications
Volume	169
Issue number	3
DOIs	https://doi.org/10.1007/s10957-015-0800-2
Publication status	Published - 1 Jun 2016

Keywords

Strictly copositive
Strictly semi-positive
Tensor complementarity
Unique solution

ASJC Scopus subject areas

Control and Optimization
Management Science and Operations Research
Applied Mathematics

More information

10.1007/s10957-015-0800-2

Cite this

@article{c794a1e17c4e40458fd6090c51a8292d,

title = "Tensor Complementarity Problem and Semi-positive Tensors",

abstract = "In this paper, we prove that a real tensor is strictly semi-positive if and only if the corresponding tensor complementarity problem has a unique solution for any nonnegative vector and that a real tensor is semi-positive if and only if the corresponding tensor complementarity problem has a unique solution for any positive vector. It is shown that a real symmetric tensor is a (strictly) semi-positive tensor if and only if it is (strictly) copositive.",

keywords = "Strictly copositive, Strictly semi-positive, Tensor complementarity, Unique solution",

author = "Yisheng Song and Liqun Qi",

year = "2016",

month = jun,

day = "1",

doi = "10.1007/s10957-015-0800-2",

language = "English",

volume = "169",

pages = "1069--1078",

journal = "Journal of Optimization Theory and Applications",

issn = "0022-3239",

publisher = "Springer New York",

number = "3",

}

TY - JOUR

T1 - Tensor Complementarity Problem and Semi-positive Tensors

AU - Song, Yisheng

AU - Qi, Liqun

PY - 2016/6/1

Y1 - 2016/6/1

N2 - In this paper, we prove that a real tensor is strictly semi-positive if and only if the corresponding tensor complementarity problem has a unique solution for any nonnegative vector and that a real tensor is semi-positive if and only if the corresponding tensor complementarity problem has a unique solution for any positive vector. It is shown that a real symmetric tensor is a (strictly) semi-positive tensor if and only if it is (strictly) copositive.

AB - In this paper, we prove that a real tensor is strictly semi-positive if and only if the corresponding tensor complementarity problem has a unique solution for any nonnegative vector and that a real tensor is semi-positive if and only if the corresponding tensor complementarity problem has a unique solution for any positive vector. It is shown that a real symmetric tensor is a (strictly) semi-positive tensor if and only if it is (strictly) copositive.

KW - Strictly copositive

KW - Strictly semi-positive

KW - Tensor complementarity

KW - Unique solution

UR - http://www.scopus.com/inward/record.url?scp=84940069045&partnerID=8YFLogxK

U2 - 10.1007/s10957-015-0800-2

DO - 10.1007/s10957-015-0800-2

M3 - Journal article

SN - 0022-3239

VL - 169

SP - 1069

EP - 1078

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

IS - 3

ER -

Tensor Complementarity Problem and Semi-positive Tensors

Abstract

Keywords

ASJC Scopus subject areas

More information

Other files and links

Fingerprint

Cite this