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In this paper, we study a bivariate distributionally robust optimization problem with mean-covariance ambiguity set and half-space support. Under a conventional type of objective function widely adopted in inventory management, option…
We study contextual stochastic optimization problems, where we leverage rich auxiliary observations (e.g., product characteristics) to improve decision making with uncertain variables (e.g., demand). We show how to train forest decision…
This paper deals with the scenario approach to robust optimization. This relies on a random sampling of the possibly infinite number of constraints induced by uncertainties in the parameters of an optimization problem. Solving the resulting…
Recent literature has advocated the use of randomized methods for accelerating the solution of various matrix problems arising throughout data science and computational science. One popular strategy for leveraging randomization is to use it…
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…
Decision-making problems can be modeled as combinatorial optimization problems with Constraint Programming formalisms such as Constrained Optimization Problems. However, few Constraint Programming formalisms can deal with both optimization…
In this paper, we consider a new problem of portfolio optimization using stochastic information. In a setting where there is some uncertainty, we ask how to best select $k$ potential solutions, with the goal of optimizing the value of the…
In this paper, we address the problem of bounding conditional expectations when moment information of the underlying distribution and the random event conditioned upon are given. To this end, we propose an adapted version of the generalized…
Reachability analysis is an important method in providing safety guarantees for systems with unknown or uncertain dynamics. Due to the computational intractability of exact reachability analysis for general nonlinear, high-dimensional…
We propose a distributionally robust data-driven predictive control framework for stochastic linear time-invariant systems with unknown dynamics and disturbance distributions. We use an offline trajectory to fit the subspace predictive…
In data-driven inverse optimization an observer aims to learn the preferences of an agent who solves a parametric optimization problem depending on an exogenous signal. Thus, the observer seeks the agent's objective function that best…
This paper considers the problem of minimizing the time average of a controlled stochastic process subject to multiple time average constraints on other related processes. The probability distribution of the random events in the system is…
Maximum likelihood estimation of Gaussian mixture models with different class-specific covariance matrices is known to be problematic. This is due to the unboundedness of the likelihood, together with the presence of spurious maximizers.…
We analyze the convergence of gradient-based optimization algorithms that base their updates on delayed stochastic gradient information. The main application of our results is to the development of gradient-based distributed optimization…
We propose a suitable analytical framework to perform numerical analysis of problems arising in compressible fluid models with uncertain data. We discuss both weak and strong stochastic approach, where the former is based on the knowledge…
Real-world distributed systems and networks are often unreliable and subject to random failures of its components. Such a stochastic behavior affects adversely the complexity of optimization tasks performed routinely upon such systems, in…
This paper develops an analytical method of truncating inequality constrained Gaussian distributed variables where the constraints are themselves described by Gaussian distributions. Existing truncation methods either assume hard…
Stochastic constraints, which incorporate both deterministic parameters and random variables, extend classical deterministic constraints by explicitly accounting for uncertainty. These constraints are increasingly prevalent in data science,…
In this study we analyze linear mixed-integer programming problems, in which the distribution of the cost vector is only observable through a finite training data set. In contrast to the related studies, we assume that the number of random…
In this paper, we consider the classic stochastic (dynamic) knapsack problem, a fundamental mathematical model in revenue management, with general time-varying random demand. Our main goal is to study the optimal policies, which can be…