# Characterization of the norm-based robust solutions in vector optimization

## TL;DR

This paper investigates the properties of norm-based robust solutions in vector optimization, introducing new directional concepts and extending characterizations to constrained problems, with implications for nonsmooth analysis.

## Contribution

It defines new non-ascent directions using Clarke's gradient and characterizes robustness in vector optimization, including constrained cases, under basic qualification conditions.

## Key findings

- Characterization of robustness via new directions
- Extension to conic constrained problems
- Necessary conditions using nonsmooth gap functions

## Abstract

In this paper, we study the norm-based robust (efficient) solutions of a Vector Optimization Problem (VOP). We define two kinds of non-ascent directions in terms of Clarke's generalized gradient and characterize norm-based robustness by means of the newly-defined directions. This is done under a basic Constraint Qualification (CQ). We extend the provided characterization to VOPs with conic constraints. Moreover, we derive a necessary condition for norm-based robustness utilizing a nonsmooth gap function.