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Stability of Solutions of Piecewise Smooth Constrained Nonlinear Equations

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  • Alexey F. Izmailov

    (Lomonosov Moscow State University (MSU))

Abstract

The paper deals with stability issues for a given solution of a piecewise smooth constrained equation under the right-hand side perturbations. We provide conditions ensuring such stability subject to large classes of perturbations, making the main accent on the cases when Robinson’s regularity condition can be violated. From a perspective of the existing literature, the main new feature of this work is a combination of reduced (i.e., piecewise) smoothness assumptions with the presence of additional constraints. Applications to reformulations of complementarity systems are also discussed.

Suggested Citation

  • Alexey F. Izmailov, 2025. "Stability of Solutions of Piecewise Smooth Constrained Nonlinear Equations," Journal of Optimization Theory and Applications, Springer, vol. 205(2), pages 1-22, May.
    • Handle: RePEc:spr:joptap:v:205:y:2025:i:2:d:10.1007_s10957-025-02650-3
    DOI: 10.1007/s10957-025-02650-3
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    References listed on IDEAS

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    1. Andreas Fischer & Markus Herrich & Alexey Izmailov & Mikhail Solodov, 2016. "Convergence conditions for Newton-type methods applied to complementarity systems with nonisolated solutions," Computational Optimization and Applications, Springer, vol. 63(2), pages 425-459, March.
    2. A. Fischer & A. F. Izmailov & M. Jelitte, 2021. "Newton-type methods near critical solutions of piecewise smooth nonlinear equations," Computational Optimization and Applications, Springer, vol. 80(2), pages 587-615, November.
    3. Andreas Fischer & Alexey F. Izmailov & Mario Jelitte, 2023. "Stability of Singular Solutions of Nonlinear Equations with Restricted Smoothness Assumptions," Journal of Optimization Theory and Applications, Springer, vol. 196(3), pages 1008-1035, March.
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