## Higher-Order Confidence Intervals for Stochastic Programming using Bootstrapping

We study the problem of constructing confidence intervals for the optimal value of a stochastic programming problem by using bootstrapping. Bootstrapping is a resampling method used in the statistical inference of unknown parameters for which only a small number of samples can be obtained. One such parameter is the optimal value of a stochastic optimization … Read more

## A Matrix-Free Approach For Solving The Gaussian Process Maximum Likelihood Problem

Gaussian processes are the cornerstone of statistical analysis in many application ar- eas. Nevertheless, most of the applications are limited by their need to use the Cholesky factorization in the computation of the likelihood. In this work, we present a matrix-free approach for comput- ing the solution of the maximum likelihood problem involving Gaussian processes. … Read more

## DIFFERENCE FILTER PRECONDITIONING FOR LARGE COVARIANCE MATRICES

In many statistical applications one must solve linear systems corresponding to large, dense, and possibly irregularly structured covariance matrices. These matrices are often ill- conditioned; for example, the condition number increases at least linearly with respect to the size of the matrix when observations of a random process are obtained from a xed domain. This … Read more

## Scalable Stochastic Optimization of Complex Energy Systems

We present a scalable approach and implementation for solving stochastic programming problems, with application to the optimization of complex energy systems under uncertainty. Stochastic programming is used to make decisions in the present while incorporating a model of uncertainty about future events (scenarios). These problems present serious computational difficulties as the number of scenarios becomes … Read more

## A Matrix-Free Approach For Solving The Gaussian Process Maximum Likelihood Problem

Gaussian processes are the cornerstone of statistical analysis in many application ar- eas. Nevertheless, most of the applications are limited by their need to use the Cholesky factorization in the computation of the likelihood. In this work, we present a matrix-free approach for comput- ing the solution of the maximum likelihood problem involving Gaussian processes. … Read more

## A Matrix-Free Approach For Solving The Gaussian Process Maximum Likelihood Problem

Gaussian processes are the cornerstone of statistical analysis in many application ar- eas. Nevertheless, most of the applications are limited by their need to use the Cholesky factorization in the computation of the likelihood. In this work, we present a matrix-free approach for comput- ing the solution of the maximum likelihood problem involving Gaussian processes. … Read more

## A Matrix-Free Approach For Solving The Gaussian Process Maximum Likelihood Problem

Gaussian processes are the cornerstone of statistical analysis in many application ar- eas. Nevertheless, most of the applications are limited by their need to use the Cholesky factorization in the computation of the likelihood. In this work, we present a matrix-free approach for comput- ing the solution of the maximum likelihood problem involving Gaussian processes. … Read more

## On the Dynamic Stability of Electricity Markets

In this work, we present new insights into the dynamic stability of electricity markets. In particular, we discuss how short forecast horizons, incomplete gaming, and physical ramping constraints can give rise to stability issues. Using basic concepts of market efficiency, Lyapunov stability, and predictive control, we construct a new stabilizing market design. A numerical case … Read more

## On the parallel solution of dense saddle-point linear systems arising in stochastic programming

We present a novel approach for solving dense saddle-point linear systems in a distributed-memory environment. This work is motivated by an application in stochastic optimization problems with recourse, but the proposed approach can be used for a large family of dense saddle-point systems, in particular those arising in convex programming. Although stochastic optimization problems have … Read more

## A preconditioning technique for Schur complement systems arising in stochastic optimization

Deterministic sample average approximations of stochastic programming problems with recourse are suitable for a scenario-based, treelike parallelization with interior-point methods and a Schur complement mechanism. However, the direct linear solves involving the Schur complement matrix are expensive, and adversely a ect the scalability of this approach. In this paper we propose a stochastic preconditioner to address … Read more