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Semidefinite relaxation bounds for bi-quadratic optimization problems with quadratic constraints

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  • Xinzhen Zhang
  • Chen Ling
  • Liqun Qi

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  • Xinzhen Zhang & Chen Ling & Liqun Qi, 2011. "Semidefinite relaxation bounds for bi-quadratic optimization problems with quadratic constraints," Journal of Global Optimization, Springer, vol. 49(2), pages 293-311, February.
    • Handle: RePEc:spr:jglopt:v:49:y:2011:i:2:p:293-311
    DOI: 10.1007/s10898-010-9545-5
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    References listed on IDEAS

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    1. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(4), pages 1007-1017, August.
    2. Jos F. Sturm & Shuzhong Zhang, 2003. "On Cones of Nonnegative Quadratic Functions," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 246-267, May.
    3. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1461-1465, December.
    4. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(1), pages 193-194, February.
    5. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(5), pages 1273-1289, October.
    6. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(3), pages 819-821, June.
    7. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(2), pages 541-545, April.
    8. Yongwei Huang & Shuzhong Zhang, 2007. "Complex Matrix Decomposition and Quadratic Programming," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 758-768, August.
    9. Anthony Man-Cho So & Yinyu Ye & Jiawei Zhang, 2008. "A Unified Theorem on SDP Rank Reduction," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 910-920, November.
    10. Gábor Pataki, 1998. "On the Rank of Extreme Matrices in Semidefinite Programs and the Multiplicity of Optimal Eigenvalues," Mathematics of Operations Research, INFORMS, vol. 23(2), pages 339-358, May.
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    Cited by:

    1. Ke Hou & Anthony Man-Cho So, 2014. "Hardness and Approximation Results for L p -Ball Constrained Homogeneous Polynomial Optimization Problems," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1084-1108, November.
    2. Shigui Li & Linzhang Lu & Xing Qiu & Zhen Chen & Delu Zeng, 2024. "Tighter bound estimation for efficient biquadratic optimization over unit spheres," Journal of Global Optimization, Springer, vol. 90(2), pages 323-353, October.
    3. Yuning Yang & Qingzhi Yang & Liqun Qi, 2014. "Approximation Bounds for Trilinear and Biquadratic Optimization Problems Over Nonconvex Constraints," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 841-858, December.
    4. Haibin Chen & Hongjin He & Yiju Wang & Guanglu Zhou, 2022. "An efficient alternating minimization method for fourth degree polynomial optimization," Journal of Global Optimization, Springer, vol. 82(1), pages 83-103, January.

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