Stochastic Programming
Distributionally Robust Optimization with General Uncertainty Structure
We develop an exact solution framework for a broad class of Distributionally Robust Optimization (DRO) problems with general uncertainty structure. Within the class of moment- and confidence-set-based ambiguity sets, existing exact methods are largely limited to max-of-affine functions under ambiguity sets with strictly nested confidence sets. To enlarge this scope while preserving tractability, we introduce … Read more
Stage-wise hybrid nested Benders’ decomposition-stochastic dual dynamic programming for virtual power plants
Participants in energy markets make sequential decisions across multiple time horizons under uncertainty, leading to large-scale multistage stochastic optimization problems. Stochastic dual dynamic programming is widely used for its tractability, but its application to modern energy markets is challenged by nested dependencies induced by participation across multiple interrelated markets under increasing uncertainty from distributed energy … Read more
Scalable Finite Adaptability via Polyhedral Partition and Learning
We study finite adaptability for decision-making under uncertainty, where a small set of candidate solutions is prepared in advance and the best response is selected after uncertainty is realized. While existing methods have made significant progress on exact formulations, scalability remains a persistent challenge due to (i) the combinatorial nature of assigning decisions to uncertainty … Read more
Relief-based Anesthesiologist Scheduling with Stochastic Surgery Durations
We present a two-stage stochastic programming model for scheduling anesthesiologists to operating rooms under uncertainty in surgery durations. The proposed model takes a relief order to balance anesthesiologists’ workload as input and captures the trade-offs between anesthesiologist relief times, handoffs and under-staffing. To address the computational challenges of solving the proposed model, we derive supervalid … Read more
Extrapolation-based Direct Search for Nonsmooth Stochastic Zeroth-Order Optimization
We propose and analyze a stochastic direct-search method for unconstrained zeroth-order minimization of locally Lipschitz, possibly nonsmooth, objectives. The method combines random polling directions with a stochastic extrapolating line search based on a sufficient-decrease test of order \(p\). Under conditional accuracy assumptions on the stochastic estimates, which can be verified for mean-zero finite-higher-moment oracle noise … Read more
Stochastic Bilevel Optimization for the Network Design of Multimodal Transit Systems with Heterogeneous Rider Preferences under Uncertain Travel Times and Demand
Designing efficient and user-friendly multimodal transit networks is critical for modern urban mobility. We study a novel stochastic multimodal transit network design problem that integrates fixed-route services with on-demand shuttles, explicitly accounting for heterogeneous rider preferences, uncertain travel times, and passenger demand. The hierarchical decision-making process is modeled using a two-stage stochastic bilevel optimization problem, … Read more
Stochastic convergence of parallel asynchronous adaptive first-order methods
A new class of asynchronous adaptive first-order optimization methods is introduced, comprising asynchronous variants of several popular algorithms. Versions of these methods using momentum and/or inexact normalization are also considered. The convergence of methods in the class on non-convex functions is analyzed in a fully stochastic setting, and is shown to be (up to logarithmic … Read more
Non-convergence Analysis of Probabilistic Direct Search
We present a non-convergence theory for probabilistic direct search, a randomized derivative-free optimization method, where non-convergence means the failure to produce iterates that achieve stationarity asymptotically. The motivation is to understand whether the submartingale-like assumption in the existing convergence theory is essential or merely an artifact of the analysis techniques. For convex objectives, we prove … Read more
Distributionally Robust Optimization via Targeted Integral Probability Metrics for General Data Processes
Distributionally robust optimization (DRO) provides a principled framework for decision-making under distributional uncertainty. Classical data-driven DRO frameworks typically construct ambiguity sets from distributional information, such as moment constraints, divergence neighborhoods, or Wasserstein balls, specified before the downstream loss is considered. We propose a task-aware DRO framework based on targeted integral probability metrics. The ambiguity set … Read more