Stability of singular solutions of nonlinear equations with restricted smoothness assumptions

Research output: Contribution to journalResearch articleContributedpeer-review



This work is concerned with conditions ensuring stability of a given solution of asystem of nonlinear equations with respect to large (not asymptotically thin) classesof right-hand side perturbations. Our main focus is on those solutions that are in a sensesingular, and hence, their stability properties are not guaranteed by “standard” inversefunction-type theorems. In the twice differentiable case, these issues have receivedsome attention in the existing literature. Moreover, a few results in this direction areknown in the case when the first derivative is merely B-differentiable. Here, we furtherelaborate on a similar setting, but the main attention is paid to the case of piecewisesmooth equations. Specifically, we study the effect of singularity of a solution for someactive smooth selection on the overall stability properties, and we provide sufficientconditions ensuring the needed stability properties in the cases when such smoothselections may exist. Finally, an application to a piecewise smooth reformulation ofcomplementarity problems is given.


Original languageEnglish
Pages (from-to)1008-1035
Number of pages28
JournalJournal of Optimization Theory and Applications
Issue number3
Publication statusPublished - Mar 2023

External IDs

Mendeley fae348af-27fd-3d10-8989-407d4a94fb38
Scopus 85146624978
WOS 000915898000001
dblp journals/jota/FischerIJ23
ORCID /0000-0002-8982-2136/work/142241994


DFG Classification of Subject Areas according to Review Boards

Subject groups, research areas, subject areas according to Destatis


  • 2-Regularity, Complementarity problem, Critical solution, Equation with Lipschitzian first derivatives, Nonisolated solution, Piecewise smooth equation, Singular solution