Related papers: A note on the complexity of two-stage stochastic l…
We study multistage distributionally robust linear optimization, where the uncertainty set is defined as a ball of distribution centered at a scenario tree using the nested distance. The resulting minimax problem is notoriously difficult to…
We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…
In this paper, we design, analyze, and implement a variant of the two-loop L-shaped algorithms for solving two-stage stochastic programming problems that arise from important application areas including revenue management and power systems.…
In this study, we consider two classes of multicriteria two-stage stochastic programs in finite probability spaces with multivariate risk constraints. The first-stage problem features a multivariate stochastic benchmarking constraint based…
We investigate a simple approximation scheme, based on overlapping linear decision rules, for solving data-driven two-stage distributionally robust optimization problems with the type-$\infty$ Wasserstein ambiguity set. Our main result…
We explore a multiple-stage variant of the min-max robust selection problem with budgeted uncertainty that includes queries. First, one queries a subset of items and gets the exact values of their uncertain parameters. Given this…
We study three two-stage optimization problems with a similar structure and different objectives. In the first stage of each problem, the goal is to assign input jobs of positive sizes to unsplittable bags. After this assignment is decided,…
We consider fundamental algorithmic number theoretic problems and their relation to a class of block structured Integer Linear Programs (ILPs) called $2$-stage stochastic. A $2$-stage stochastic ILP is an integer program of the form $\min…
Adaptive robust optimization problems are usually solved approximately by restricting the adaptive decisions to simple parametric decision rules. However, the corresponding approximation error can be substantial. In this paper we show that…
In this paper we extend the well-known L-Shaped method to solve two-stage stochastic programming problems with decision-dependent uncertainty. The method is based on a novel, unifying, formulation and on distribution-specific optimality and…
First-order stochastic methods are the state-of-the-art in large-scale machine learning optimization owing to efficient per-iteration complexity. Second-order methods, while able to provide faster convergence, have been much less explored…
We study two-stage stochastic optimization problems with random recourse, where the adaptive decisions are multiplied with the uncertain parameters in both the objective function and the constraints. To mitigate the computational…
Recently, there has been a growing interest in distributionally robust optimization (DRO) as a principled approach to data-driven decision making. In this paper, we consider a distributionally robust two-stage stochastic optimization…
We study the computational complexity of the optimal transport problem that evaluates the Wasserstein distance between the distributions of two K-dimensional discrete random vectors. The best known algorithms for this problem run in…
Two-stage robust optimization problems constitute one of the hardest optimization problem classes. One of the solution approaches to this class of problems is K-adaptability. This approach simultaneously seeks the best partitioning of the…
We introduce a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic mixed integer linear optimization problems with recourse. The framework highlights the common mathematical…
Two-stage stochastic programming is a popular framework for optimization under uncertainty, where decision variables are split between first-stage decisions, and second-stage (or recourse) decisions, with the latter being adjusted after…
We consider bilevel linear problems, where the right-hand side of the lower level problems is stochastic. The leader has to decide in a here-and-now fashion, while the follower has complete information. In this setting, the leader's outcome…
Decision making needs to take an uncertain environment into account. Over the last decades, robust optimization has emerged as a preeminent method to produce solutions that are immunized against uncertainty. The main focus in robust…
We study two-stage adjustable robust linear programming in which the right-hand sides are uncertain and belong to a convex, compact uncertainty set. This problem is NP-hard, and the affine policy is a popular, tractable approximation. We…