Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these estimators as the sample size goes to infinity, which is both of theoretical as well as practical interest. This area of … Read more
We consider a multiperiod stochastic capacitated facility location problem under uncertain demand and budget in each period. Using a scenario tree representation of the uncertainties, we formulate a multistage stochastic integer program to dynamically locate facilities in each period and compare it with a two-stage approach that determines the facility locations up front. In the … Read more
In this paper, we develop an algorithm to efficiently solve risk-averse optimization problems posed in reflexive Banach space. Such problems often arise in many practical applications as, e.g., optimization problems constrained by partial differential equations with uncertain inputs. Unfortunately, for many popular risk models including the coherent risk measures, the resulting risk-averse objective function is … Read more
Day-ahead scheduling of electricity generation or unit commitment is an important and challenging optimization problem in power systems. Variability in net load arising from the increasing penetration of renewable technologies have motivated study of various classes of stochastic unit commitment models. In two-stage models, the generation schedule for the entire day is fixed while the … Read more
Resource allocation models in contingency planning aim to mitigate unexpected failures in supply chains due to disruptions with rare occurrence but disastrous consequences. This paper formulates this problems as a two-stage stochastic optimization with a risk-averse recourse function, and proposes a novel computationally tractable solution approach. The method relies on an inexact bundle method and … Read more
In this paper we consider the notion of rectangularity of a set of probability measures, introduced in Epstein and Schneider (2003), from a somewhat different point of view. We define rectangularity as a property of dynamic decomposition of a distributionally robust stochastic optimization problem and show how it relates to the modern theory of coherent … Read more
We formulate a risk-averse multi-stage stochastic program using conditional value at risk as the risk measure. The underlying random process is assumed to be stage-wise independent, and a stochastic dual dynamic programming (SDDP) algorithm is applied. We discuss the poor performance of the standard upper bound estimator in the risk-averse setting and propose a new … Read more
In this paper we discuss time consistency of risk averse multistage stochastic programming problems. We show, in a framework of finite scenario trees, that composition of law invariant coherent risk measures can be law invariant only for the expectation or max-risk measures. CitationPreprintArticleDownload View PDF
In this paper we discuss statistical properties and rates of convergence of the Stochastic Dual Dynamic Programming (SDDP) method applied to multistage linear stochastic programming problems. We assume that the underline data process is stagewise independent and consider the framework where at first a random sample from the original (true) distribution is generated and consequently … Read more
In this paper we discuss time consistency of multi-stage risk averse stochastic programming problems. We approach the concept of time consistency from an optimization point of view. That is, at each state of the system optimality of a decision policy should not involve states which cannot happen in the future. We also discuss a relation … Read more