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Stability analysis of split equality and split feasibility problems

Author

Listed:
  • Vu Thi Huong

    (Zuse Institute Berlin
    Vietnam Academy of Science and Technology)

  • Hong-Kun Xu

    (Hangzhou Dianzi University
    Henan Normal University)

  • Nguyen Dong Yen

    (Vietnam Academy of Science and Technology)

Abstract

In this paper, for the first time in the literature, we study the stability of solutions of two classes of feasibility (i.e., split equality and split feasibility) problems by set-valued and variational analysis techniques. Our idea is to equivalently reformulate the feasibility problems as parametric generalized equations to which set-valued and variational analysis techniques apply. Sufficient conditions, as well as necessary conditions, for the Lipschitz-likeness of the involved solution maps are proved by exploiting special structures of the problems and by using an advanced result of B.S. Mordukhovich [J. Global Optim. 28, 347–362 (2004)]. These conditions stand on a solid interaction among all the input data by means of their dual counterparts, which are transposes of matrices and regular/limiting normal cones to sets. Several examples are presented to illustrate how the obtained results work in practice and also show that the assumption on the existence of a nonzero solution used in the necessity conditions cannot be lifted.

Suggested Citation

  • Vu Thi Huong & Hong-Kun Xu & Nguyen Dong Yen, 2025. "Stability analysis of split equality and split feasibility problems," Journal of Global Optimization, Springer, vol. 92(2), pages 411-429, June.
    • Handle: RePEc:spr:jglopt:v:92:y:2025:i:2:d:10.1007_s10898-025-01469-6
    DOI: 10.1007/s10898-025-01469-6
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    References listed on IDEAS

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    1. Chen Chen & Ting Kei Pong & Lulin Tan & Liaoyuan Zeng, 2020. "A difference-of-convex approach for split feasibility with applications to matrix factorizations and outlier detection," Journal of Global Optimization, Springer, vol. 78(1), pages 107-136, September.
    2. Biao Qu & Binghua Liu, 2018. "The Split Feasibility Problem and Its Solution Algorithm," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-7, January.
    3. Jean-Pierre Aubin, 1984. "Lipschitz Behavior of Solutions to Convex Minimization Problems," Mathematics of Operations Research, INFORMS, vol. 9(1), pages 87-111, February.
    4. Haitao Che & Yaru Zhuang & Yiju Wang & Haibin Chen, 2023. "A relaxed inertial and viscosity method for split feasibility problem and applications to image recovery," Journal of Global Optimization, Springer, vol. 87(2), pages 619-639, November.
    5. Le Hai Yen & Nguyen Thi Thanh Huyen & Le Dung Muu, 2019. "A subgradient algorithm for a class of nonlinear split feasibility problems: application to jointly constrained Nash equilibrium models," Journal of Global Optimization, Springer, vol. 73(4), pages 849-868, April.
    Full references (including those not matched with items on IDEAS)

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