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Error Bounds for the Solution Sets of Quadratic Complementarity Problems

Author

Listed:
  • Shenglong Hu

    (Hangzhou Dianzi University)

  • Jie Wang

    (China Jiliang University)

  • Zheng-Hai Huang

    (Tianjin University)

Abstract

In this article, two types of fractional local error bounds for quadratic complementarity problems are established, one is based on the natural residual function and the other on the standard violation measure of the polynomial equalities and inequalities. These fractional local error bounds are given with explicit exponents. A fractional local error bound with an explicit exponent via the natural residual function is new in the tensor/polynomial complementarity problems literature. The other fractional local error bounds take into account the sparsity structures, from both the algebraic and the geometric perspectives, of the third-order tensor in a quadratic complementarity problem. They also have explicit exponents, which improve the literature significantly.

Suggested Citation

  • Shenglong Hu & Jie Wang & Zheng-Hai Huang, 2018. "Error Bounds for the Solution Sets of Quadratic Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 983-1000, December.
    • Handle: RePEc:spr:joptap:v:179:y:2018:i:3:d:10.1007_s10957-018-1356-8
    DOI: 10.1007/s10957-018-1356-8
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    References listed on IDEAS

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    1. Yisheng Song & Gaohang Yu, 2016. "Properties of Solution Set of Tensor Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 85-96, July.
    2. Zheng-Hai Huang & Liqun Qi, 2017. "Formulating an n-person noncooperative game as a tensor complementarity problem," Computational Optimization and Applications, Springer, vol. 66(3), pages 557-576, April.
    3. Jie Wang & Shenglong Hu & Zheng-Hai Huang, 2018. "Solution Sets of Quadratic Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 120-136, January.
    4. Chen Ling & Hongjin He & Liqun Qi, 2016. "On the cone eigenvalue complementarity problem for higher-order tensors," Computational Optimization and Applications, Springer, vol. 63(1), pages 143-168, January.
    5. Yisheng Song & Liqun Qi, 2016. "Tensor Complementarity Problem and Semi-positive Tensors," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 1069-1078, June.
    6. Xue-Li Bai & Zheng-Hai Huang & Yong Wang, 2016. "Global Uniqueness and Solvability for Tensor Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 72-84, July.
    7. Maolin Che & Liqun Qi & Yimin Wei, 2016. "Positive-Definite Tensors to Nonlinear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 475-487, February.
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    Citations

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    Cited by:

    1. Zheng-Hai Huang & Liqun Qi, 2019. "Tensor Complementarity Problems—Part I: Basic Theory," Journal of Optimization Theory and Applications, Springer, vol. 183(1), pages 1-23, October.
    2. Tong-tong Shang & Guo-ji Tang, 2023. "Structured tensor tuples to polynomial complementarity problems," Journal of Global Optimization, Springer, vol. 86(4), pages 867-883, August.
    3. Bui Dinh & Tien-Son Pham, 2022. "Error Bounds of Regularized Gap Functions for Polynomial Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 226-247, January.
    4. Vu Trung Hieu & Yimin Wei & Jen-Chih Yao, 2020. "Notes on the Optimization Problems Corresponding to Polynomial Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 687-695, February.
    5. Shouqiang Du & Weiyang Ding & Yimin Wei, 2021. "Acceptable Solutions and Backward Errors for Tensor Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 188(1), pages 260-276, January.
    6. Xue-Li Bai & Zheng-Hai Huang & Xia Li, 2019. "Stability of Solutions and Continuity of Solution Maps of Tensor Complementarity Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(02), pages 1-19, April.
    7. Meng-Meng Zheng & Zheng-Hai Huang & Xiao-Xiao Ma, 2020. "Nonemptiness and Compactness of Solution Sets to Generalized Polynomial Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 80-98, April.
    8. Tong-tong Shang & Jing Yang & Guo-ji Tang, 2022. "Generalized Polynomial Complementarity Problems over a Polyhedral Cone," Journal of Optimization Theory and Applications, Springer, vol. 192(2), pages 443-483, February.

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