Volume 2005
Recent Submissions

20051229BuchDecomposing CVaR minimization in twostage stochastic models Based on the polyhedral representation of KünziBay and Mayer (2005), we propose a decomposition framework for the minimization of CVaR in twostage stochastic models.We show that the decomposed problems can be effectively ...

20051229BuchA Comparative Study of Decomposition Algorithms for Stochastic Combinatorial Optimization This paper presents comparative computational results using three decomposition algorithms on a battery of instances drawn from three different applications. In order to preserve the commonalities among the algorithms in ...

20051228BuchAggregation and Discretization in Multistage Stochastic Programming Multistage stochastic programs have applications in many areas and support policy makers in finding rational decisions that hedge against unforeseen neg ative events. In order to ensure computational tractability, ...

20050830BuchAmbiguous chance constrained problems and robust optimization In this paper we study ambiguous chance constrained problems where the distributions of the random parameters in the problem are themselves uncertain. We focus primarily on the special case where the uncertainty set Q of ...

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 ...

20050706BuchThe value of multistage stochastic programming in capacity planning under uncertainty This paper addresses a general class of capacity planning problems under uncertainty, which arises, for example, in semiconductor tool purchase planning. Using a scenario tree to model the evolution of the uncertainties, ...

20050706BuchA Stochastic Gradient Type Algorithm for Closed Loop Problems We focus on solving closedloop stochastic problems, and propose a perturbed gradient algorithm to achieve this goal. The main hurdle in such problems is the fact that the control variables are infinite dimensional, and ...

20050621BuchStructural Properties of Linear Probabilistic Constraints The paper provides a structural analysis of the feasible set defined by linear probabilistic constraints. Emphasis is laid on single (individual) probabilistic constraints. A classical convexity result by Van de Panna/Popp ...

20050428BuchAdaptive and nonadaptive samples in solving stochastic linear programs A computational investigationLarge scale stochastic linear programs are typically solved using a combination of mathematical programming techniques and samplebased approximations. Some methods are designed to permit sample sizes to adapt to information ...

20050426BuchLipschitz and differentiability properties of quasiconcave and singular normal distribution functions The paper provides a condition for differentiability as well as an equivalent criterion for Lipschitz continuity of singular normal distributions. Such distributions are of interest, for instance, in stochastic optimization ...

20050411BuchConvex approximations for a class of mixedinteger recourse models We consider mixedinteger recourse (MIR) models with a single recourse constraint. We relate the secondstage value function of such problems to the expected simple integer recourse (SIR) shortage function. This allows to ...

20050411BuchNotes on free lunch in the limit and pricing by conjugate duality theory King and Korf introduced, in the framework of a discretetime dynamic market model on a general probability space, a new concept of arbitrage called free lunch in the limit which is slightly weaker than the common free ...

20050411BuchExtending algebraic modelling languages for Stochastic Programming The algebraic modelling languages (AML) have gained wide acceptance and use in Mathematical Programming by researchers and practitioners. At a basic level, stochastic programming models can be defined using these languages ...

20050311BuchTwostage stochastic semidefinite programming and decomposition based interior point methods TheoryWe introduce two stage stochastic semidefinite programs with recourse and present a Benders decomposition based linearly convergent interior point algorithm to solve them. This extends the results in Zhao [16] wherein it ...

20050225BuchStochastic integer programming Limit theorems and confidence intervalsWe consider empirical approximations of twostage stochastic mixedinteger programs and derive central limit theorems for the objectives and optimal values. The limit theorems are based on empirical process theory and the ...

20050225BuchAssessing Solution Quality in Stochastic Programs Determining whether a solution is of high quality (optimal or near optimal) is a fundamental question in optimization theory and algorithms. In this paper, we develop Monte Carlo samplingbased procedures for assessing ...

20050112BuchStress Testing for VaR an CVaR Practical use of the contamination technique in stress testing for risk measures Value at Risk (VaR) and Conditional Value at Risk (CVaR) and for optimization problems with these risk criteria is discussed. Whereas for ...

20050110BuchA BranchReduceCut Algorithm for the Global Optimization of Probabilistically Constrained Linear Programs We consider probabilistic constrained linear programs with general distributions for the uncertain parameters. These problems generally involve nonconvex feasible sets. We develop a branch and bound algorithm that searches ...

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 ...