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An Extension of Yuan’s Lemma to Fourth-Order Tensor System

Author

Listed:
  • Qingzhi Yang

    (Kashgar University
    Nankai University)

  • Yang Zhou

    (Nankai University)

  • Yuning Yang

    (Guangxi University)

Abstract

Yuan’s lemma is a basic proposition on homogeneous quadratic function systems. In this note, we extend Yuan’s lemma to the fourth-order tensor system. We first give generalized definition of positive semidefinite of fourth-order tensor, and based on it, an extension of Yuan’s lemma is proposed. As an application, we establish the strong duality result of a class of quadratic semidefinite programming problems using the extended Yuan’s lemma.

Suggested Citation

  • Qingzhi Yang & Yang Zhou & Yuning Yang, 2019. "An Extension of Yuan’s Lemma to Fourth-Order Tensor System," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 803-810, March.
    • Handle: RePEc:spr:joptap:v:180:y:2019:i:3:d:10.1007_s10957-018-1378-2
    DOI: 10.1007/s10957-018-1378-2
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    References listed on IDEAS

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    1. B. T. Polyak, 1998. "Convexity of Quadratic Transformations and Its Use in Control and Optimization," Journal of Optimization Theory and Applications, Springer, vol. 99(3), pages 553-583, December.
    2. Sheng-Long Hu & Zheng-Hai Huang, 2012. "Theorems of the Alternative for Inequality Systems of Real Polynomials," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 1-16, July.
    3. Shenglong Hu & Guoyin Li & Liqun Qi, 2016. "A Tensor Analogy of Yuan’s Theorem of the Alternative and Polynomial Optimization with Sign structure," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 446-474, February.
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