Multi-period distributionally robust optimization (DRO) is in general not time consistent. For a given multi-period DRO problem with generalized moments ambiguity, we propose an Ambiguity Updating Robust Architecture (AURA) that constructs the ambiguity set of all conditional distributions-to-go, given the realized uncertainty. We prove that AURA is time consistent, but is more conservative than the … Read more
We study two-stage facility location in which the probability of each demand scenario is an affine function of the opening decisions, so the objective multiplies a decision-dependent probability by a decision-dependent recourse value and is bilinear in the binary first stage. The standard treatment linearizes these products with McCormick envelopes over global bounds on the … Read more
Explainability is a growing concern for optimization models used as decision-making tools. It aims to help a stakeholder understand why a model recommends a given outcome, typically by exhibiting the elements of the input that account for this outcome. We study this question for linear two-stage stochastic programs, and explain the returned decision by a … Read more
Distributionally robust optimization (DRO) minimizes worst-case risk under distributional uncertainty, but its decisions can be suboptimal in terms of their excess risk, or regret. We study this gap for multivariate least-squares regression, assuming that the observed source law and unknown target law differ by an adversarial 2-Wasserstein perturbation of size \(\varepsilon\). We first identify the … Read more
Performative decision-making arises in many real-world problems where decisions influence the populations that generate future data. A major line of existing research focuses on learning performatively stable solutions. We study average-reward performative optimization, where the learner observes an evolving population through sample batches of fixed size and learns from a single continuing trajectory with unknown … Read more
We study nonconvex stochastic functions that admit a structured second-order representation, a generalization of lower- and upper-C² functions to normal integrands. Similarly to the deterministic case, lower-C² normal integrands are defined as the pointwise maxima over a compact random index set of functions that are twice-continuously differentiable in the decision variable with an integrable bounded … Read more
We consider multistage stochastic mixed-integer programs M-SMIPs, and show that these problems are asymptotically convex. That is, we show that the expected cost-to-go functions in the problem converge to convex functions as the variability of the random parameters in the model increases. To derive this result, we first propose a novel adapted Gomory relaxation for … Read more
A stochastic proximal-gradient method is proposed and analyzed for solving regularized optimization problems subject to nonlinear equality constraints and nonnegativity bounds. The objective function’s values and gradients are available only through inexact stochastic oracles. The method decomposes each trial step into one component that reduces linearized infeasibility and a second component that seeks optimality while … Read more
Matrix assembly layouts provide manufacturing flexibility under product variety and demand volatility through locally reconfigurable production stations. Periodic redesign exploits this flexibility, yet existing models allow only annual revisions. Finer calendars expose a flexibility-commitment trade-off: advance layout commitments support coordination, supplier agreements, and discounts. We introduce the layout revision timing problem, jointly choosing revision points … Read more
Distributionally robust optimization hedges a decision against an ambiguity set of candidate distributions. In a cold-start setting the target distribution is unobserved and no sample from it is available, so only related source distributions provide evidence for constructing that set. We propose an inclusive-exclusive Wasserstein ball model that jointly learns a center and radius from … Read more