2023/11/28 by Nguyen Duy Cuong, Cuong, Nguyen Duy
Computer Science · Mathematics · #49J52 #49J53 (Primary) 49K40 #90C30 #90C46 (Secondary) #Advanced Optimization Algorithms Research #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2311.16731
openalex publication_date 2023/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper extends the well-known Lyusternik-Graves theorem for set-valued mappings to the Holder framework, offers an affirmative answer to an open problem proposed by Dontchev and improves recent results of He and Ng. Primal and dual necessary and sufficient conditions for Holder metric regularity are established. The results are applied to convergence analysis of a Newton-type method. Some open problems for future research are also discussed.