The work was funded by the Volkswagen Foundation, by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 409756759, and by the Russian Foundation for Basic Research Grants 19-51-12003 NNIO_a and 20-01-00106.
Abstract
For many years, local Lipschitzian error bounds for systems of equations have been successfully used for the design and analysis of Newton-type methods. There are characterizations of those error bounds by means of first-order derivatives like a recent result by Izmailov, Kurennoy, and Solodov on critical solutions of nonlinear equations. We aim at extending this result in two directions which shall enable, to some extent, to include additional constraints and to consider mappings with reduced smoothness requirements. This leads to new necessary as well as sufficient conditions for the existence of error bounds.
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Dedicated to Professor R. Tyrrell Rockafellar on the occasion of his 85th birthday.
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Fischer, A., Izmailov, A.F. & Jelitte, M. Constrained Lipschitzian Error Bounds and Noncritical Solutions of Constrained Equations. Set-Valued Var. Anal 29, 745–765 (2021). https://doi.org/10.1007/s11228-020-00568-8
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DOI: https://doi.org/10.1007/s11228-020-00568-8
Keywords
- Constrained equation
- constrained error bound
- critical and noncritical solutions
- (piecewise) semidifferentiable functions