Geometry of the Copositive Tensor Cone and its Dual

Man-Man Dong () and Hai-Bin Chen
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Man-Man Dong: School of Management Science, Qufu Normal University, Rizhao, Shandong 276800, P. R. China
Hai-Bin Chen: School of Management Science, Qufu Normal University, Rizhao, Shandong 276800, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2020, vol. 37, issue 04, 1-11

Abstract: In this paper, we explore some geometric properties of the cones in terms of extreme rays, exposed rays, the exposed face and the maximal face. To this end, we first show that all copositive tensors orthogonal to the generating tensor of the exposed ray in completely positive tensor cone construct a maximal face of the copositive tensor cone, then give a characterization on the maximal face of the copositive tensor cone. Third, we show that each extreme ray of the completely positive tensor cone is an exposed ray in the even order case. Finally, we give a lower bound and an upper bound for the maximal face of the completely positive tensor cone.

Keywords: Copositive tensor cone; extreme ray; exposed face; maximal face (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0217595920400084

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