Near Convexity and Generalized Differentiation

Authors

Nguyen Mau Nam, Portland State UniversityFollow
Nguyen Nang Thieu, Vietnam Academy of Science and Technology
Nguyen Dong Yen, Vietnam Academy of Science and Technology

Published In

Journal of Convex Analysis

Document Type

Pre-Print

Publication Date

3-16-2025

Subjects

Convex sets

Abstract

In this paper, we introduce the concept of nearly convex set-valued mappings and investigate fundamental properties of these mappings. Additionally, we establish a geometric approach for generalized differentiation of nearly convex set-valued mappings and nearly convex functions. Our contributions expand the current knowledge of nearly convex sets and functions, while providing several new results pertaining to nearly convex set-valued mappings.

Rights

This is the author manuscript subsequently published in the Journal of Convex Analysis 32 (2025), No. 2, 605-630. Copyright Heldermann Verlag 2025

Description

AMS subject classifications. 49J52, 49J53, 90C31

DOI

10.48550/arXiv.2302.08986

Persistent Identifier

https://archives.pdx.edu/ds/psu/43153

Citation Details

Nam, N. M., Thieu, N. N., & Yen, N. D. (2023). Near convexity and generalized differentiation. arXiv preprint arXiv:2302.08986.