Stability of Solutions of Piecewise Smooth Constrained Nonlinear Equations

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 condi...

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Bibliographic Details
Published inJournal of optimization theory and applications Vol. 205; no. 2; p. 40
Main Author Izmailov, Alexey F.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.05.2025
Springer Nature B.V
Subjects
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Constraints
Engineering
Mathematics
Mathematics and Statistics
Nonlinear equations
Operations Research/Decision Theory
Optimization
Perturbation
Smoothness
Stability
Theory of Computation
Constrained equation
Stability
Nonisolated solution
49J52
90C33
Piecewise smooth equation
47J07
Covering
Complementarity problem
47J05
Regularity
2-regularity
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-025-02650-3