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Optimality conditions based on the Fréchet second-order subdifferential

Author

Listed:
  • D. T. V. An

    (Thai Nguyen University of Sciences)

  • N. D. Yen

    (Vietnam Academy of Science and Technology)

Abstract

This paper focuses on second-order necessary optimality conditions for constrained optimization problems on Banach spaces. For problems in the classical setting, where the objective function is $$C^2$$ C 2 -smooth, we show that strengthened second-order necessary optimality conditions are valid if the constraint set is generalized polyhedral convex. For problems in a new setting, where the objective function is just assumed to be $$C^1$$ C 1 -smooth and the constraint set is generalized polyhedral convex, we establish sharp second-order necessary optimality conditions based on the Fréchet second-order subdifferential of the objective function and the second-order tangent set to the constraint set. Three examples are given to show that the used hypotheses are essential for the new theorems. Our second-order necessary optimality conditions refine and extend several existing results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:81:y:2021:i:2:d:10.1007_s10898-021-01011-4
    DOI: 10.1007/s10898-021-01011-4
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    References listed on IDEAS

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    1. 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.
    2. Nguyen Ngoc Luan & Jen-Chih Yao, 2019. "Generalized polyhedral convex optimization problems," Journal of Global Optimization, Springer, vol. 75(3), pages 789-811, November.
    3. Nguyen Dong Yen & Xiaoqi Yang, 2018. "Affine Variational Inequalities on Normed Spaces," Journal of Optimization Theory and Applications, Springer, vol. 178(1), pages 36-55, July.
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    Cited by:

    1. Duong Thi Viet An, 2022. "Second-Order Optimality Conditions for Infinite-Dimensional Quadratic Programs," Journal of Optimization Theory and Applications, Springer, vol. 192(2), pages 426-442, February.

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