Work

Continuous Selections and Invertibility of Nonsmooth Maps Between Banach Spaces

Year: 2025

Type: article

Abstract: In the setting of Banach spaces, we address the problems of local surjectivity, existence of a continuous selection and invertibility for nonsmooth maps which admit a suitable pseudo-Jacobian. We obtain a general sufficient condition for the existence of a continuous selection. As a consequence, we recover from our result the classical Bartle-Graves selection theorem for linear maps. We also obtain a sufficient condition for local invertibility, which in particular applies to certain Gâteaux differentiable maps.

Source: Journal of Optimization Theory and Applications

DOI: 10.1007/s10957-025-02692-7

Authors: Milen Ivanov, Jesús A. Jaramillo, Sebastián Lajara, Nadia Zlateva

Institutions: Universidad Complutense de Madrid, Institute of Mathematical Sciences, Sofia University "St. Kliment Ohridski"

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190