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Model uncertainties and simulation uncertainties occur in mathematical modeling of multiscale complex systems, since some mechanisms or scales are not represented (i.e., "unresolved") due to lack in our understanding of these mechanisms or…
Latent variable models have been playing a central role in psychometrics and related fields. In many modern applications, the inference based on latent variable models involves one or several of the following features: (1) the presence of…
Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic…
Column-sparse packing problems arise in several contexts in both deterministic and stochastic discrete optimization. We present two unifying ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain improved approximation…
We propose an approach to compute inner and outer-approximations of the sets of values satisfying constraints expressed as arbitrarily quantified formulas. Such formulas arise for instance when specifying important problems in control such…
While Robust Model Predictive Control considers the worst-case system uncertainty, Stochastic Model Predictive Control, using chance constraints, provides less conservative solutions by allowing a certain constraint violation probability…
In this extended abstract, we report on ongoing work towards an approximate multimodal optimization algorithm with asymptotic guarantees. Multimodal optimization is the problem of finding all local optimal solutions (modes) to a path…
Model-based process simulation can be used to derive designs and operating conditions of chemical processes that optimally balance multiple objectives, such as quality, costs, or environmental impacts. This work focuses on identifying…
In this paper we study the optimality of the certainty equivalence approximation in robust finite-horizon optimization problems with expected cost. We provide an algorithm for determining the subset of the state-space for which the…
We propose a novel distribution-free scheme to solve optimization problems where the goal is to minimize the expected value of a cost function subject to probabilistic constraints. Unlike standard sampling-based methods, our idea consists…
This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…
We give an $\alpha(1+\epsilon)$-approximation algorithm for solving covering LPs, assuming the presence of a $(1/\alpha)$-approximation algorithm for a certain optimization problem. Our algorithm is based on a simple modification of the…
Optimization under uncertainty deals with the problem of optimizing stochastic cost functions given some partial information on their inputs. These problems are extremely difficult to solve and yet pervade all areas of technological and…
We study approximability of regular constraint satisfaction problems, i.e., CSPs where each variable in an instance has the same number of occurrences. In particular, we show that for any CSP $\Lambda$, existence of an $\alpha$…
We study the approximability of two related machine scheduling problems. In the late work minimization problem, there are identical parallel machines and the jobs have a common due date. The objective is to minimize the late work, defined…
This article is devoted to propose some lower and upper bounds for the coupled-tasks scheduling problem in presence of compatibility constraints according to classical complexity hypothesis ($\mathcal{P} \neq \mathcal{NP}$,…
Robust optimization provides a principled and unified framework to model many problems in modern operations research and computer science applications, such as risk measures minimization and adversarially robust machine learning. To use a…
In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…
We consider the problem of makespan minimization on unrelated machines when job sizes are stochastic. The goal is to find a fixed assignment of jobs to machines, to minimize the expected value of the maximum load over all the machines. For…
In this paper, we study the following robust optimization problem. Given an independence system and candidate objective functions, we choose an independent set, and then an adversary chooses one objective function, knowing our choice. Our…