# Minimizers of Gerstewitz functionals

## TL;DR

This paper investigates the properties of minimizer sets of Gerstewitz functionals in vector optimization, providing conditions for their nonemptiness and compactness, and exploring their interdependencies and implications for scalarization methods.

## Contribution

It offers new conditions for the existence and compactness of minimizer sets and links Gerstewitz functional minimization to a generalized scalarization approach.

## Key findings

- Conditions for nonempty minimizer sets
- Criteria for compactness of solutions
- Interdependencies between solutions with different parameters

## Abstract

Scalarization in vector optimization is essentially based on the minimization of Gerstewitz functionals. In this paper, the minimizer sets of Gerstewitz functionals are investigated. Conditions are given under which such a set is nonempty and compact. Interdependencies between solutions of problems with different parameters or with different feasible point sets are shown. Consequences for the parameter control in scalarization methods are derived. It is pointed out that the minimization of Gerstewitz functionals is equivalent to an optimization problem which generalizes the scalarization by Pascoletti and Serafini.