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Kurdyka-Łojasiewicz inequality and error bounds of D-Gap functions for nonsmooth and nonmonotone variational inequality problems

Author

Listed:
  • M. H. Li

    (Chongqing University of Arts and Sciences, School of Mathematics and Big Data)

  • K. W. Meng

    (Southwestern University of Finance and Economics, School of Mathematics and Big Data Laboratory on Financial Security and Behavior)

  • X. Q. Yang

    (The Hong Kong Polytechnic University, Department of Applied Mathematics)

Abstract

In this paper, we study regularized/D-gap functions associated with a nonsmooth and nonmonotone variational inequality problem. We present some exact formulas for the subderivative, the regular subdifferential, and the limiting subdifferential of the regularized/D-gap functions respectively. By virtue of these formulas, we provide some sufficient conditions and necessary conditions for the Kurdyka-Łojasiewicz inequality property and the error bound property for the D-gap function respectively. As an application of our Kurdyka-Łojasiewicz inequality result, we show that, under certain mild assumptions, the sequence generated by a derivative-free descent algorithm with an inexact line search converges linearly to a solution of the variational inequality problem.

Suggested Citation

  • M. H. Li & K. W. Meng & X. Q. Yang, 2025. "Kurdyka-Łojasiewicz inequality and error bounds of D-Gap functions for nonsmooth and nonmonotone variational inequality problems," Journal of Global Optimization, Springer, vol. 93(3), pages 833-860, November.
    • Handle: RePEc:spr:jglopt:v:93:y:2025:i:3:d:10.1007_s10898-025-01558-6
    DOI: 10.1007/s10898-025-01558-6
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