14 papers · 1 filter
Lipschitzian SLLNs for random functions
Lai Tian, Johannes O. Royset
We prove strong laws of large numbers for locally Lipschitz functions in the Lipschitz pseudometric. Our results hold under either a topological or a model-theoretic condition, wit…
Perturbation Duality for Robust and Distributionally Robust Optimization: Short and General Proofs
Louis L. Chen, Jake Roth, Johannes O. Royset
Duality is a foundational tool in robust and distributionally robust optimization (RO/DRO), underpinning both analytical insights and tractable reformulations. Whereas RO/DRO duali…
Failure of uniform laws of large numbers for subdifferentials and beyond
Lai Tian, Johannes O. Royset
We provide counterexamples showing that uniform laws of large numbers do not hold for subdifferentials under natural assumptions. Our constructions are univariate random Lipschitz…
Composite Optimization using Local Models and Global Approximations
Welington de Oliveira, Johannes O. Royset
This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems,…
Optimistic Bilevel Optimization with Composite Lower-Level Problem
Mattia Solla, Johannes O. Royset
This paper introduces a novel double regularization scheme for bilevel optimization problems whose lower-level problem is composite and convex, but not necessarily strongly convex,…
Rockafellian Relaxation for PDE-Constrained Optimization with Distributional Uncertainty
Harbir Antil, Sean P. Carney, Hugo DÃaz +1
Stochastic optimization problems are generally known to be ill-conditioned to the form of the underlying uncertainty. A framework is introduced for optimal control problems with pa…