Convergence Analysis of the Gauss–Newton-Type Method for Lipschitz-Like Mappings
We introduce in the present paper a Gauss–Newton-type method for solving generalized equations defined by sums of differentiable mappings and set-valued mappings in Banach spaces. Semi-local convergence and local convergence of the Gauss–Newton-type method are analyzed.
KeywordsSet-valued mappings Lipschitz-like mappings Generalized equations Gauss–Newton-type method Semi-local convergence
The authors thank the referees and the associate editor for their valuable comments and constructive suggestions which improved the presentation of this manuscript. Research work of the first author is fully supported by Chinese Scholarship Council, and research work of the third author is partially supported by National Natural Science Foundation (grant 11171300) and Zhejiang Provincial Natural Science Foundation (grant Y6110006) of China.
- 19.Mordukhovich, B.S.: Variational Analysis and Generalized Differentiation I: Basic Theory. Springer, Berlin (2006) Google Scholar
- 21.Mordukhovich, B.S.: Sensitivity analysis in nonsmooth optimization. In: Field, D.A., Komkov, V. (eds.) Theoretical Aspects of Industrial Design. SIAM Proc. Appl. Math., vol. 58, pp. 32–46 (1992) Google Scholar