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Geometry of the Copositive Tensor Cone and its Dual

Author

Listed:
  • 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)

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.

Suggested Citation

  • Man-Man Dong & Hai-Bin Chen, 2020. "Geometry of the Copositive Tensor Cone and its Dual," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(04), pages 1-11, August.
    • Handle: RePEc:wsi:apjorx:v:37:y:2020:i:04:n:s0217595920400084
    DOI: 10.1142/S0217595920400084
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