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Quadratic Growth and Strong Metric Subregularity of the Subdifferential for a Class of Non-prox-regular Functions

Author

Listed:
  • Nguyen Huy Chieu

    (Vinh University)

  • Nguyen Thi Quynh Trang

    (Vinh University)

  • Ha Anh Tuan

    (Ho Chi Minh City University of Transport)

Abstract

This paper mainly studies the quadratic growth and the strong metric subregularity of the subdifferential of a function that can be represented as the sum of a function twice differentiable in the extended sense and a subdifferentially continuous, prox-regular, twice epi-differentiable function. For such a function, which is not necessarily prox-regular, it is shown that the quadratic growth, the strong metric subregularity of the subdifferential at a local minimizer, and the positive definiteness of the subgradient graphical derivative at a stationary point are equivalent. In addition, other characterizations of the quadratic growth and the strong metric subregularity of the subdifferential are also given. Besides, properties of functions twice differentiable in the extended sense are examined.

Suggested Citation

  • Nguyen Huy Chieu & Nguyen Thi Quynh Trang & Ha Anh Tuan, 2022. "Quadratic Growth and Strong Metric Subregularity of the Subdifferential for a Class of Non-prox-regular Functions," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 1081-1106, September.
    • Handle: RePEc:spr:joptap:v:194:y:2022:i:3:d:10.1007_s10957-022-02071-6
    DOI: 10.1007/s10957-022-02071-6
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    References listed on IDEAS

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    1. Yunier Bello-Cruz & Guoyin Li & Tran T. A. Nghia, 2021. "On the Linear Convergence of Forward–Backward Splitting Method: Part I—Convergence Analysis," Journal of Optimization Theory and Applications, Springer, vol. 188(2), pages 378-401, February.
    2. Nguyen T. V. Hang & Boris S. Mordukhovich & M. Ebrahim Sarabi, 2022. "Augmented Lagrangian method for second-order cone programs under second-order sufficiency," Journal of Global Optimization, Springer, vol. 82(1), pages 51-81, January.
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