Newton-type methods near critical solutions of piecewise smooth nonlinear equations

Artikel

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Journal: Computational Optimization and Applications ; ISSN: 1573-2894 ; Volume: 80 ; Year: 2021 ; Issue: 2 ; Pages: 587-615 ; New York, NY: Springer US

Classification and Topics

• Classification: Mathematik ; Dispute Resolution: Strikes, Arbitration, and Mediation; Collective Bargaining ; Labor-Management Relations; Industrial Jurisprudence ; Civil Law; Common Law ; Multiple or Simultaneous Equation Models: Panel Data Models; Spatio-temporal Models
• Subject: Piecewise smooth equation ; Constrained equation ; Complementarity problem ; Singular solution ; Critical solution ; 2-regularity

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Fischer, A. ; Izmailov, A. F. ; Jelitte, M.
• Event: Veröffentlichung
• (who): Springer US
• (where): New York, NY
• (when): 2021

Further information

• DOI: doi:10.1007/s10589-021-00306-2
• Last update: 10.03.2025, 11:43 AM CET