Related papers: Chance-constrained optimization with tight confide…

This paper proposes a robust approximation method for solving chance constrained optimization (CCO) of polynomials. Assume the CCO is defined with an individual chance constraint that is affine in the decision variables. We construct a…

Conventional inverse optimization inputs a solution and finds the parameters of an optimization model that render a given solution optimal. The literature mostly focuses on inferring the objective function in linear problems when accepted…

We consider the problem of choosing design parameters to minimize the probability of an undesired rare event that is described through the average of $n$ iid random variables. Since the probability of interest for near optimal design…

We analyse the convergence of the proximal gradient algorithm for convex composite problems in the presence of gradient and proximal computational inaccuracies. We derive new tighter deterministic and probabilistic bounds that we use to…

Inference after model selection has been an active research topic in the past few years, with numerous works offering different approaches to addressing the perils of the reuse of data. In particular, major progress has been made recently…

Constraints can be interpreted in a broad sense as any kind of explicit restriction over the parameters. While some constraints are defined directly on the parameter space, when they are instead defined by known behaviour on the model,…

In this paper, we consider robust control using randomized algorithms. We extend the existing order statistics distribution theory to the general case in which the distribution of population is not assumed to be continuous and the order…

The Laplace approximation is a popular method for constructing a Gaussian approximation to the Bayesian posterior and thereby approximating the posterior mean and variance. But approximation quality is a concern. One might consider using…

Scenario optimization and conformal prediction share a common goal, that is, turning finite samples into safety margins. Yet, different terminology often obscures the connection between their respective guarantees. This paper revisits that…

This paper introduces a framework for Chance-Constrained Optimization with Complex Variables, addressing complex linear programming for both individual and joint probabilistic constraints in the complex domain. We first analyze the 3CP…

In this paper we consider non-smooth convex optimization problems with (possibly) infinite intersection of constraints. In contrast to the classical approach, where the constraints are usually represented as intersection of simple sets,…

We propose an open loop methodology based on sample statistics to solve chance constrained stochastic optimal control problems with probabilistic safety guarantees for linear systems where the additive Gaussian noise has unknown mean and…

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 target the problem of accuracy and robustness in causal inference from finite data sets. Some state-of-the-art algorithms produce clear output complete with solid theoretical guarantees but are susceptible to propagating erroneous…

We revisit the sample average approximation (SAA) approach for non-convex stochastic programming. We show that applying the SAA approach to problems with expected value equality constraints does not necessarily result in asymptotic…

We study stochastic optimization problems with chance and risk constraints, where in the latter, risk is quantified in terms of the conditional value-at-risk (CVaR). We consider the distributionally robust versions of these problems, where…

We study system design problems stated as parameterized stochastic programs with a chance-constraint set. We adopt a Bayesian approach that requires the computation of a posterior predictive integral which is usually intractable. In…

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…

Computing the probability of evidence even with known error bounds is NP-hard. In this paper we address this hard problem by settling on an easier problem. We propose an approximation which provides high confidence lower bounds on…

The upper bounds on the coverage probabilities of the confidence regions based on blockwise empirical likelihood [Kitamura (1997)] and nonstandard expansive empirical likelihood [Nordman et al. (2013)] methods for time series data are…