Related papers: A note on the complexity of two-stage stochastic l…

The paper considers distributed stochastic optimization over randomly switching networks, where agents collaboratively minimize the average of all agents' local expectation-valued convex cost functions. Due to the stochasticity in gradient…

We address two sets of long-standing open questions in probability theory, from a computational complexity perspective: divisibility of stochastic maps, and divisibility and decomposability of probability distributions. We prove that finite…

We address high-dimensional zero-one random parameters in two-stage convex conic optimization problems. Such parameters typically represent failures of network elements and constitute rare, high-impact random events in several applications.…

Bilevel optimization has been widely applied in many important machine learning applications such as hyperparameter optimization and meta-learning. Recently, several momentum-based algorithms have been proposed to solve bilevel optimization…

Many discrete optimization problems are amenable to constrained shortest-path reformulations in an extended network space, a technique that has been key in convexification, bound strengthening, and search. In this paper, we propose a…

We study systems of String Equations where block variables need to be assigned strings so that their concatenation gives a specified target string. We investigate this problem under a multivariate complexity framework, searching for…

In high-dimensional data analysis, bi-level sparsity is often assumed when covariates function group-wisely and sparsity can appear either at the group level or within certain groups. In such cases, an ideal model should be able to…

Progressive Hedging is a popular decomposition algorithm for solving multi-stage stochastic optimization problems. A computational bottleneck of this algorithm is that all scenario subproblems have to be solved at each iteration. In this…

The problem of approximating a dense matrix by a product of sparse factors is a fundamental problem for many signal processing and machine learning tasks. It can be decomposed into two subproblems: finding the position of the non-zero…

We first show a simple but striking result in bilevel optimization: unconstrained $C^\infty$ smooth bilevel programming is as hard as general extended-real-valued lower semicontinuous minimization. We then proceed to a worst-case analysis…

We unify and extend the semigroup and the PDE approaches to stochastic maximal regularity of time-dependent semilinear parabolic problems with noise given by a cylindrical Brownian motion. We treat random coefficients that are only…

The main focus of this paper is radius-based (supplier) clustering in the two-stage stochastic setting with recourse, where the inherent stochasticity of the model comes in the form of a budget constraint. In addition to the standard…

We propose a novel approach using supervised learning to obtain near-optimal primal solutions for two-stage stochastic integer programming (2SIP) problems with constraints in the first and second stages. The goal of the algorithm is to…

Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…

Smart distribution grids should efficiently integrate stochastic renewable resources while effecting voltage regulation. The design of energy management schemes is challenging, one of the reasons being that energy management is a multistage…

In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…

In bilevel optimization problems, a leader and a follower make their decisions in a hierarchy, and both decisions may influence each other. Usually one assumes that both players have full knowledge also of the other player's data. In a more…

In two-stage robust optimization the solution to a problem is built in two stages: In the first stage a partial, not necessarily feasible, solution is exhibited. Then the adversary chooses the "worst" scenario from a predefined set of…

Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…

This paper considers the scheduling of stochastic jobs on parallel identical machines to minimize the expected total weighted completion time. While this is a classical problem with a significant body of research on approximation algorithms…