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New Second-Order Optimality Conditions for a Class of Differentiable Optimization Problems

Author

Listed:
  • Nguyen Quang Huy

    (Hanoi Pedagogical University No. 2)

  • Nguyen Van Tuyen

    (Hanoi Pedagogical University No. 2)

Abstract

In the present paper, we focus on the optimization problems, where objective functions are Fréchet differentiable, and whose gradient mapping is locally Lipschitz on an open set. We introduce the concept of second-order symmetric subdifferential and its calculus rules. By using the second-order symmetric subdifferential, the second-order tangent set and the asymptotic second-order tangent cone, we establish some second-order necessary and sufficient optimality conditions for optimization problems with geometric constraints. Examples are given to illustrate the obtained results.

Suggested Citation

  • Nguyen Quang Huy & Nguyen Van Tuyen, 2016. "New Second-Order Optimality Conditions for a Class of Differentiable Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 27-44, October.
    • Handle: RePEc:spr:joptap:v:171:y:2016:i:1:d:10.1007_s10957-016-0980-4
    DOI: 10.1007/s10957-016-0980-4
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    Cited by:

    1. D. T. V. An & N. D. Yen, 2021. "Optimality conditions based on the Fréchet second-order subdifferential," Journal of Global Optimization, Springer, vol. 81(2), pages 351-365, October.
    2. G. Haeser & A. Ramos, 2020. "New Constraint Qualifications with Second-Order Properties in Nonlinear Optimization," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 494-506, February.
    3. Giorgio Giorgi, 2019. "Notes on Constraint Qualifications for Second-Order Optimality Conditions," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 11(5), pages 16-32, October.

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