Work

Decision Space Decomposition for Multiobjective Optimization

Year: 2026

Type: article

Abstract: Being inspired by the parametric decomposition theorem for multiobjective optimization problems (MOPs) of Cuenca Mira and Miguel García (2017), and by the block-coordinate descent method for single objective optimization problems, we present a decomposition theorem for computing the set of minimal elements of a partially ordered set. This set is decomposed into subsets whose minimal elements are used to retrieve the overall minimal elements. We apply this approach to convex MOPs decomposing their decision space into lines and prove the set convergence of this method in the Painlevé-Kuratowski sense. A special case for biobjective quadratic optimization problems is included.

Source: Journal of Optimization Theory and Applications

DOI: 10.1007/s10957-025-02924-w

Authors: Emma Soriano, Mishko Mitkovski, Margaret M. Wiecek

Institution: Clemson University

Language: English

Topic: Advanced Multi-Objective Optimization Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Clemson University