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SDP relaxation algorithms for $$\mathbf {P}(\mathbf {P}_0)$$P(P0)-tensor detection

Author

Listed:
  • Xiao Wang

    (Tianjin University)

  • Xinzhen Zhang

    (Tianjin University)

  • Guangming Zhou

    (Xiangtan University)

Abstract

$$\mathbf {P}$$P-tensor and $$\mathbf {P}_0$$P0-tensor are introduced in tensor complementarity problem, which have wide applications in game theory. In this paper, we establish SDP relaxation algorithms for detecting $$\mathbf {P}(\mathbf {P}_0)$$P(P0)-tensor. We first reformulate $$\mathbf {P}(\mathbf {P}_0)$$P(P0)-tensor detection problem as polynomial optimization problems. Then we propose the SDP relaxation algorithms for solving the reformulated polynomial optimization problems. Numerical examples are reported to show the efficiency of the proposed algorithms.

Suggested Citation

  • Xiao Wang & Xinzhen Zhang & Guangming Zhou, 2020. "SDP relaxation algorithms for $$\mathbf {P}(\mathbf {P}_0)$$P(P0)-tensor detection," Computational Optimization and Applications, Springer, vol. 75(3), pages 739-752, April.
    • Handle: RePEc:spr:coopap:v:75:y:2020:i:3:d:10.1007_s10589-019-00145-2
    DOI: 10.1007/s10589-019-00145-2
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    References listed on IDEAS

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    2. Laurent, M., 2009. "Sums of squares, moment matrices and optimization over polynomials," Other publications TiSEM 9fef820b-69d2-43f2-a501-e, Tilburg University, School of Economics and Management.
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