2023/09/21 by Amos Uderzo, Uderzo, Amos
Engineering · Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Mathematical and Theoretical Analysis #Optimization and Control (math.OC) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2309.12277
openalex publication_date 2023/09/21 · openalex created_date 2023/09/23 · openalex updated_date 2026/07/28
A recognized trend of research investigates generalizations of the Hadamard's inversion theorem to functions that may fail to be differentiable. In this vein, the present paper explores some consequences of a recent result about the existence of global Lipschitz continuous inverse by translating its metric assumptions in terms of nonsmooth analysis constructions. This exploration focuses on continuous, but possibly not locally Lipschitz mappings, acting in finite-dimensional Euclidean spaces. As a result, sufficient conditions for global invertibility are formulated by means of strict estimators, *-difference of convex compacta and regular/basic coderivatives. These conditions qualify the global inverse as a Lipschitz continuous mapping and provide quantitative estimates of its Lipschitz constant in terms of the above constructions.