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This approach demonstrates set convergence of minimal elements in convex multiobjective optimization, suggesting efficient solutions for complex problems.
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.
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Soriano et al. (2026) studied this question.
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