Work

Multi-Objective Optimization and its Connection to Multivariate Risk Measures

Year: 2026

Type: article

Abstract: In this paper, we generalize the study of minimax stochastic programming to the case where the objective function is multi-objective. We adopt a component -wise worst-case approach and provide necessary and sufficient conditions for optimality in terms of suitable first-order conditions. We then compare the proposed method with the minimization of vector -valued risk measures, as developed progressively in the literature over the past decades. We show that minimizing a certain class of multivariate risk measures is, in a precise sense, equivalent to solving a multi-objective expected value optimization problem with respect to some appropriate admissible distributions. We also analyze specific optimization problems involving risk functionals.

Source: Journal of Optimization Theory and Applications

DOI: 10.1007/s10957-026-02978-4

Authors: Elisa Mastrogiacomo, Matteo Rocca, Marco Tarsia

Institution: University of Insubria

Language: English

Topic: Risk and Portfolio Optimization

Subfield: Management Science and Operations Research

Field: Decision Sciences

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Università degli Studi dell'Insubria, Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni