Browsing Stochastic Programming Eprint Series (SPEPS) by Title
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20101020BuchSamplingbased decomposition methods for riskaverse multistage programs We define a risk averse nonanticipative feasible policy for multistage stochastic programsand propose a methodology to implement it. The approach is based on dynamic programmingequations written for a risk averse formulation ...

20170221BuchScenariao Reduction Revisited: Fundamental Limits and Gurarantees The goal of scenario reduction is to approximate a given discrete distributionwith another discrete distribution that has fewer atoms. We distinguishcontinuous scenario reduction, where the new atoms may be chosen freely, ...

20061026BuchScenario reduction in stochastic programming with respect to discrepancy distances Discrete approximations to chance constrained and mixedinteger twostage stochastic programs require moderately sized scenario sets. The relevant distances of (multivariate) probability distributions for deriving quantitative ...

20000814BuchScenario reduction in stochastic programming: An approach using probability metrics Given a convex stochastic programming problem with a discrete initial probability distribution, the problem of optimal scenario reduction is stated as follows: Determine a scenario subset of prescribed cardinality and a ...

20060331BuchScenario tree modelling for multistage stochastic programs An important issue for solving multistage stochastic programs consists inthe approximate representation of the (multivariate) stochastic input process inthe form of a scenario tree. In this paper, forward and backward ...

20080405BuchScenario tree reduction for multistage stochastic programs A framework for the reduction of scenario trees as inputs of (linear) multistage stochastic programs is provided such that optimal values and approximate solution sets remain close to each other. The argument is based on ...

20120409BuchSDDP for multistage stochastic linear programs based on spectral risk measures We consider riskaverse formulations of multistage stochastic linear programs. Forthese formulations, based on convex combinations of spectral risk measures, riskaverse dynamicprogramming equations can be written. As a ...

20010416BuchSecondorder lower bounds on the expectation of a convex function We develop a class of lower bounds on the expectation of a convex function. The bounds utilize the first two moments of the underlying random variable, whose support is contained in a bounded interval or hyperrectangle. ...

20070603BuchSecondOrder Stochastic Dominance Constraints Induced by MixedInteger Linear Recourse We introduce stochastic integer programs with dominance constraints induced by mixedinteger linear recourse. Closedness of the constraint set mapping with respect to perturbations of the underlying probability measure is ...

20070708BuchSelfconcordant Tree and Decomposition Based Interior Point Methods for Stochastic Convex Optimization Problem We consider barrier problems associated with two and multistage stochastic convex optimization problems. We show that the barrier recourse functions at any stage form a selfconcordant family with respect to the barrier ...

20061207BuchShapebased Scenario Generation using Copulas The purpose of this article is to show how the multivariate structure (the ”shape” of the distribution) can be separated from the marginal distributions when generating scenarios. To dothis we use the copula. As a result, ...

20061027BuchShortterm hydropower production planning by stochastic programming Within the framework of multistage mixedinteger linear stochastic programmingwe develop a shortterm production plan for a pricetaking hydropower plant operating under uncertainty. Current production must comply with ...

20050110BuchSimple Integer Recourse Models Convexity and Convex ApproximationsWe consider the objective function of a simple recourse problem with fixed technology matrix and integer secondstage variables. Separability due to the simple recourse structure allows to study a onedimensional version ...

20030621BuchSimplification of recourse models by modification of recourse data We consider modification of the recourse data, consisting of the secondstage parameters and the underlying distribution, as an approximation technique for solving twostage recourse problems. This approach is applied to ...

20061027BuchSome remarks on valueatrisk optimization We discuss two observations related to valueatarisk optimization. First we consider a portfolio problem under an infinite number of valueatrisk inequality constraints (modelling first order stochastic dominance). The ...

20100525BuchStability and sensitivity analysis of stochastic programs with second order dominance constraints In this paper we present stability and sensitivity analysis of a stochastic optimizationproblem with stochastic second order dominance constraints. We consider perturbation of theunderlying probability measure in the space ...

20050808BuchStability of multistage stochastic programs Quantitative stability of linear multistage stochastic programs is studied. It is shown that the infima of such programs behave (locally) Lipschitz continuous with respect to the sum of an $L_r$distance and of a distance ...

20061214BuchStability of multistage stochastic programs incorporating polyhedral risk measures We analyse stability aspects of linear multistage stochastic programs with polyhedral risk measures inthe objective. In particular, we consider sensitivity of the optimal value with respect perturbations ofthe underlying ...

20060621BuchStability of εapproximate solutions to convex stochastic programs An analysis of convex stochastic programs is provided if the underlying probability distribution is subjected to (small) perturbations. It is shown, in particular,that εapproximate solution sets of convex stochastic ...

20150512BuchStatistical Estimation of Composite Risk Functionals and Risk Optimization Problems We address the statistical estimation of composite functionals whichmay be nonlinear in the probability measure. Our study is motivated bythe need to estimate coherent measures of risk, which become increasinglypopular in ...