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Strong subdifferentials: theory and applications in nonconvex optimization

Author

Listed:
  • A. Kabgani

    (Urmia University of Technology)

  • F. Lara

    (Universidad de Tarapacá)

Abstract

A new subdifferential for dealing with nonconvex functions is provided in the following paper and the usual properties are presented as well. Furthermore, characterizations and optimality conditions for a point to be a solution for the nonconvex minimization problem are given. In particular, new KKT-type optimality conditions for nonconvex nonsmooth constraint optimization problems are developed. Moreover, a relationship with the proximity operator for lower semicontinuous quasiconvex functions is given and, as a consequence, the nonemptiness of this subdifferential for large classes of quasiconvex functions is ensured.

Suggested Citation

  • A. Kabgani & F. Lara, 2022. "Strong subdifferentials: theory and applications in nonconvex optimization," Journal of Global Optimization, Springer, vol. 84(2), pages 349-368, October.
    • Handle: RePEc:spr:jglopt:v:84:y:2022:i:2:d:10.1007_s10898-022-01149-9
    DOI: 10.1007/s10898-022-01149-9
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    References listed on IDEAS

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    1. Dinh The Luc & Michel Théra, 1994. "Derivatives with Support and Applications," Mathematics of Operations Research, INFORMS, vol. 19(3), pages 659-675, August.
    2. Vial, Jean-Philippe, 1982. "Strong convexity of sets and functions," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 187-205, January.
    3. Felipe Lara & Alireza Kabgani, 2021. "On global subdifferentials with applications in nonsmooth optimization," Journal of Global Optimization, Springer, vol. 81(4), pages 881-900, December.
    4. F. Lara, 2022. "On Strongly Quasiconvex Functions: Existence Results and Proximal Point Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 192(3), pages 891-911, March.
    5. VIAL, Jean-Philippe, 1982. "Strong convexity of sets and functions," LIDAM Reprints CORE 475, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Jean-Philippe Vial, 1983. "Strong and Weak Convexity of Sets and Functions," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 231-259, May.
    7. Alberto Cambini & Laura Martein, 2009. "Generalized Convexity and Optimization," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-70876-6, December.
    8. Kabgani, Alireza & Soleimani-damaneh, Majid, 2022. "Semi-quasidifferentiability in nonsmooth nonconvex multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 299(1), pages 35-45.
    9. VIAL, Jean-Philippe, 1983. "Strong and weak convexity of sets and functions," LIDAM Reprints CORE 529, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. R. T. Rockafellar, 1981. "Proximal Subgradients, Marginal Values, and Augmented Lagrangians in Nonconvex Optimization," Mathematics of Operations Research, INFORMS, vol. 6(3), pages 424-436, August.
    11. Alireza Kabgani & Majid Soleimani-damaneh & Moslem Zamani, 2017. "Optimality conditions in optimization problems with convex feasible set using convexificators," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(1), pages 103-121, August.
    12. Satoshi Suzuki, 2021. "Karush–Kuhn–Tucker type optimality condition for quasiconvex programming in terms of Greenberg–Pierskalla subdifferential," Journal of Global Optimization, Springer, vol. 79(1), pages 191-202, January.
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