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We consider a variant of the set covering problem with uncertain parameters, which we refer to as the chance-constrained set multicover problem (CC-SMCP). In this problem, we assume that there is uncertainty regarding whether a selected set…

In this paper, we study the distributionally robust joint chance constrained Markov decision process. {Utilizing the logarithmic transformation technique,} we derive its deterministic reformulation with bi-convex terms under the…

Many stochastic optimization problems include chance constraints that enforce constraint satisfaction with a specific probability; however, solving an optimization problem with chance constraints assumes that the solver has access to the…

We propose a randomized method for solving linear programs with a large number of columns but a relatively small number of constraints. Since enumerating all the columns is usually unrealistic, such linear programs are commonly solved by…

The scenario-based optimization approach (`scenario approach') provides an intuitive way of approximating the solution to chance-constrained optimization programs, based on finding the optimal solution under a finite number of sampled…

This paper looks at two problems, minimum constrained input selection and minimum cost constrained input selection for state space structured systems. The input matrix is constrained in the sense that the set of states that each input can…

An optimization problem considering AC power flow constraints and integer decision variables can usually be posed as a mixed-integer quadratically constrained quadratic program (MIQCQP) problem. In this paper, first, a set of valid linear…

In this paper, we develop a distributionally robust chance-constrained formulation of the Optimal Power Flow problem (OPF) whereby the system operator can leverage contextual information. For this purpose, we exploit an ambiguity set based…

This paper considers the problem of minimizing a convex expectation function over a closed convex set, coupled with a set of inequality convex expectation constraints. We present a new stochastic approximation type algorithm, namely the…

This article considers the challenge of accommodating outlier measurements in state estimation. The Risk-Averse Performance-Specified (RAPS) state estimation approach addresses outliers as a measurement selection Bayesian risk minimization…

Large multiple-input multiple-output (MIMO) networks promise high energy efficiency, i.e., much less power is required to achieve the same capacity compared to the conventional MIMO networks if perfect channel state information (CSI) is…

In this paper, we consider the canonical water network design problem, which contains nonconvex potential loss functions and discrete resistance choices with varying costs. Traditionally, to resolve the nonconvexities of this problem,…

To address the challenges of imbalanced multi-class datasets typically used for rare event detection in critical cyber-physical systems, we propose an optimal, efficient, and adaptable mixed integer programming (MIP) ensemble weighting…

Uncertainties from deepening penetration of renewable energy resources have posed critical challenges to the secure and reliable operations of future electric grids. Among various approaches for decision making in uncertain environments,…

We study the sample complexity of the plug-in approach for learning $\varepsilon$-optimal policies in average-reward Markov decision processes (MDPs) with a generative model. The plug-in approach constructs a model estimate then computes an…

Single-level reformulations of (non-convex) distributionally robust optimization (DRO) problems are often intractable, as they contain semiinfinite dual constraints. Based on such a semiinfinite reformulation, we present a safe…

In this paper we propose a stochastic model predictive control (MPC) algorithm for linear discrete-time systems affected by possibly unbounded additive disturbances and subject to probabilistic constraints. Constraints are treated in…

The problem of sampling constrained continuous distributions has frequently appeared in many machine/statistical learning models. Many Monte Carlo Markov Chain (MCMC) sampling methods have been adapted to handle different types of…

We consider the Chance Constrained Model Predictive Control problem for polynomial systems subject to disturbances. In this problem, we aim at finding optimal control input for given disturbed dynamical system to minimize a given cost…

In Part I (arXiv:1911.00619) of this article, we proposed an importance sampling algorithm to compute rare-event probabilities in forward uncertainty quantification problems. The algorithm, which we termed the "Bayesian Inverse Monte Carlo…