Folklore in Multi-Objective Optimisation

TL;DR

This paper reviews and rigorously proves several well-known but informally accepted results in multi-objective optimisation, extending their applicability and clarifying their proofs.

Contribution

It transfers and generalizes folklore results in multi-objective optimisation, providing rigorous and comprehensive proofs for previously informal or case-specific results.

Findings

Generalized folklore results in multi-objective optimisation

Provided rigorous proofs for previously informal results

Extended applicability of known results to broader settings

Abstract

In this paper, we present and prove some results in multi-objective optimisation that are considered folklore. For the most part, proofs for these results exist in special cases, but they are used in more general settings since their proofs can be (largely) transferred. We do this transfer explicitly and try to state the results as generally as possible. In particular, we also aim at providing clean and complete proofs for results where the original papers are not rigorous.