On Subregularity Properties of Set-Valued Mappings. Applications to Solid Vector Optimization

TL;DR

This paper classifies at-point regularities of set-valued mappings, explores their relationships, and applies subregularity properties to derive implicit theorems and solve multicriteria optimization problems.

Contribution

It introduces a classification of regularity properties, analyzes their relationships, and applies these concepts to implicit theorems and multicriteria optimization.

Findings

Classification of at-point regularities

Relationships between regularity properties

Applications to multicriteria optimization

Abstract

In this work we classify the at-point regularities of set-valued mappings into two categories and then we analyze their relationship through several implications and examples. After this theoretical tour, we use the subregularity properties to deduce implicit theorems for set-valued maps. Finally, we present some applications to the study of multicriteria optimization problems.