set convergence – Optimization Online

Statistical Consistency of Distributionally Robust Optimization

Published: 2026/04/15, Updated: 2026/04/22

Robust Optimization, Stochastic Programming distributionally robust optimization, PK convergence, set convergence, Statistical consistency

We study the statistical consistency of distributionally robust optimization (DRO) with metric-based ambiguity sets. While convergence of optimal values is well understood, a unified set-valued analysis of feasible regions and solution sets remains largely missing, especially for constrained DRO. We develop a general variational framework based on a collapse principle, which requires that all probability … Read more

Limits of eventual families of sets with application to algorithms for the common fixed point problem

Published: 2022/03/08

Yair Censor

Eliahu Levy

Convex Optimization, Nonlinear Optimization common fixed points, cutters, eventual families, firmly nonexpansive operators, Hausdorff topological space, multifamily, multiset, set convergence

We present an abstract framework for asymptotic analysis of convergence based on the notions of eventual families of sets that we define. A family of subsets of a given set is called here an “eventual family” if it is upper hereditary with respect to inclusion. We define accumulation points of eventual families in a Hausdorff … Read more