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Error Bounds of Regularized Gap Functions for Polynomial Variational Inequalities

Author

Listed:
  • Bui Dinh

    (Le Quy Don Technical University
    Institue of Mathematics, VAST)

  • Tien-Son Pham

    (Dalat University)

Abstract

This paper is devoted to presenting new error bounds of regularized gap functions for polynomial variational inequalities with exponents explicitly determined by the dimension of the underlying space and the number/degree of the involved polynomials. The main techniques are based on semialgebraic geometry and variational analysis, which allow us to establish a nonsmooth extension of the seminal Łojasiewicz gradient inequality to regularized gap functions with explicitly calculated exponents.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:192:y:2022:i:1:d:10.1007_s10957-021-01960-6
    DOI: 10.1007/s10957-021-01960-6
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    References listed on IDEAS

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    1. L.R. Huang & K. F. Ng, 2005. "Equivalent Optimization Formulations and Error Bounds for Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 125(2), pages 299-314, May.
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    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. 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.
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