Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/287045 
Year of Publication: 
2021
Citation: 
[Journal:] Computational Optimization and Applications [ISSN:] 1573-2894 [Volume:] 80 [Issue:] 2 [Publisher:] Springer US [Place:] New York, NY [Year:] 2021 [Pages:] 587-615
Publisher: 
Springer US, New York, NY
Abstract: 
It is well-recognized that in the presence of singular (and in particular nonisolated) solutions of unconstrained or constrained smooth nonlinear equations, the existence of critical solutions has a crucial impact on the behavior of various Newton-type methods. On the one hand, it has been demonstrated that such solutions turn out to be attractors for sequences generated by these methods, for wide domains of starting points, and with a linear convergence rate estimate. On the other hand, the pattern of convergence to such solutions is quite special, and allows for a sharp characterization which serves, in particular, as a basis for some known acceleration techniques, and for the proof of an asymptotic acceptance of the unit stepsize. The latter is an essential property for the success of these techniques when combined with a linesearch strategy for globalization of convergence. This paper aims at extensions of these results to piecewise smooth equations, with applications to corresponding reformulations of nonlinear complementarity problems.
Subjects: 
Piecewise smooth equation
Constrained equation
Complementarity problem
Singular solution
Critical solution
2-regularity
JEL: 
J52
J53
K15
C33
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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