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<p>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.</p>

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Stability of Solutions of Piecewise Smooth Constrained Nonlinear Equations

  • 期刊论文

  • 发表日期：

    2025年4月2日

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  • Alexey F. Izmailov

摘要

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.