Newton's method for generalized equations: a sequential implicit function theorem

• 成果类型: Article; Proceedings Paper
• 署名作者: Dontchev, A. L.; Rockafellar, R. T.
• 署名单位: National Science Foundation (NSF); NSF - Directorate for Mathematical & Physical Sciences (MPS); NSF - Division of Mathematical Sciences (DMS); University of Washington; University of Washington Seattle
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-009-0322-5
• 发表日期: 2010
• 页码: 139-159
• 关键词: mesh-independence; STABILITY

摘要

In an extension of Newton's method to generalized equations, we carry further the implicit function theorem paradigm and place it in the framework of a mapping acting from the parameter and the starting point to the set of all associated sequences of Newton's iterates as elements of a sequence space. An inverse function version of this result shows that the strong regularity of the mapping associated with the Newton sequences is equivalent to the strong regularity of the generalized equation mapping.