Newton's method for fully parameterized generalized equations. (2nd November 2018)

• Record Type: Journal Article
• Authors: Ouyang, Wei; Zhang, Binbin
• Is Part Of: Optimization. Volume 67:Number 11(2018)
• Page Start: 2061
• Page End: 2080
• Publication Date: 2018-11-02
• Subjects: Newton's method -- generalized equation -- (partial) metric regularity -- (partial) Lipschitz-like property; 49J53 -- 65J15 -- 90C31; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1512605
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, our efforts are dedicated to study the application of Newton's method to a fully parameterized generalized equation in which both single-valued and set-valued functions depend on the parameter. We established results concerning parametric properties of the associated sequences of Newton's iterates, which follows the general format of the implicit function theorem paradigm.