Painlevé-Kuratowski convergence – Optimization Online

Asymptotic Consistency of Data-Driven Distributionally Robust Optimization via Reference-Distribution Convergence and Ambiguity-Set Shrinkage

Published: 2026/04/15, Updated: 2026/05/07

Robust Optimization, Stochastic Programming Ambiguity-set shrinkage, data-driven optimization, distributionally robust optimization, Painlevé-Kuratowski convergence, Statistical consistency

We study asymptotic consistency of data-driven distributionally robust optimization with shrinking ambiguity sets. The analysis separates reference-distribution convergence from ambiguity-set shrinkage on a prescribed test-function class. Under compactness and continuity assumptions, this yields uniform convergence of robust objectives, optimal-value convergence, and outer convergence of minimizers. For constrained DRO, the same mechanism gives uniform convergence of … Read more

Decision space decomposition for multiobjective optimization

Published: 2025/03/23, Updated: 2025/03/31

Emma Soriano

Margaret Wiecek

Mishko Mitkovski

Multi-Criteria Optimization efficient set, line-search, Painlevé-Kuratowski convergence, pareto set, vector optimization

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 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 … Read more