Browsing Stochastic Programming Eprint Series (SPEPS) by Title
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20000321BuchRandom lsc functions ScalarizationRandom lsc (lower semicontinuous) functions can be indentified with a vectorvalued random variable by means of an appropriate scalarization. It is shown that stationarity, ergodicity and independence properties are preserved ...

20000207BuchRandom lsc functions An ergodic theoremAn ergodic theorem for random lsc functions is obtained by relying on a (novel) 'scalarization' of such functions. In the process, Kolmogorov's extension theorem for randon lsc functions is established. Applications to ...

20100604BuchReformulation of general chance constrained problems using the penalty functions We explore reformulation of nonlinear stochastic programs with several joint chance constraints by stochastic programs with suitably chosenpenaltytype objectives. We show that the two problems are asymptotically equivalent. ...

20020816BuchRisk aversion via excess probabilities in stochastic programs with mixedinteger recourse We consider linear twostage stochastic programs with mixedinteger recourse. Instead of basing the selection of an optimal firststage solution on expected costs alone, we include into the objective a risk term reflecting ...

20011004BuchRisk measures for income streams A new measure of risk is introduced for a sequence of random incomes adapted to some filtration. This measure is formulated as the optimal net present value of a stream of adaptively planned commitments for consumption. ...

20150916BuchRisk measures for vectorvalued returns Portfolios, which are exposed to different currencies, have separate and different returns ineach individual currency and are thus vectorvalued in a natural way.This paper investigates the natural domain of these risk ...

20091016BuchRiskAverse TwoStage Stochastic LinearProgramming: Modeling and Decomposition We formulate a riskaverse twostage stochastic linear programming problem in which unresolved uncertainty remains after the second stage. The objective function is formulated as a composition of conditional risk measures.We ...

20000327BuchRobust path choice in networks with failures The problem of adaptive routing in a network with failures is considered. The network may be in one of finitely many states characterized by different travel times along the arcs, and transitions between the states occur ...

20061027BuchRobust solution and risk measures for a supply chain planning problem under uncertainty We consider a strategic supply chain planning problem formulated as a twostageStochastic Integer Programming (SIP) model. The strategic decisions include sitelocations, choices of production, packing and distribution ...

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, ...