Browsing Volume 2005 by Title
Now showing items 1-19 of 19
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2005-01-10BuchA Branch-Reduce-Cut 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 non-convex feasible sets. We develop a branch and bound algorithm that searches ...
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2005-12-29BuchA 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 ...
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2005-07-06BuchA Stochastic Gradient Type Algorithm for Closed Loop Problems We focus on solving closed-loop 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 ...
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2005-04-28BuchAdaptive and nonadaptive samples in solving stochastic linear programs Large scale stochastic linear programs are typically solved using a combination of mathematical programming techniques and sample-based approximations. Some methods are designed to permit sample sizes to adapt to information ...
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2005-12-28BuchAggregation 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, ...
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2005-08-30BuchAmbiguous 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 ...
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2005-02-25BuchAssessing 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 sampling-based procedures for assessing ...
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2005-04-11BuchConvex approximations for a class of mixed-integer recourse models We consider mixed-integer recourse (MIR) models with a single recourse constraint. We relate the second-stage value function of such problems to the expected simple integer recourse (SIR) shortage function. This allows to ...
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2005-12-29BuchDecomposing CVaR minimization in two-stage stochastic models Based on the polyhedral representation of Künzi-Bay and Mayer (2005), we propose a decomposition framework for the minimization of CVaR in two-stage stochastic models.We show that the decomposed problems can be effectively ...
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2005-04-11BuchExtending 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 ...
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2005-04-26BuchLipschitz and differentiability properties of quasi-concave 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 ...
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2005-04-11BuchNotes on free lunch in the limit and pricing by conjugate duality theory King and Korf introduced, in the framework of a discrete-time 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 ...
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2005-01-10BuchSimple Integer Recourse Models We consider the objective function of a simple recourse problem with fixed technology matrix and integer second-stage variables. Separability due to the simple recourse structure allows to study a one-dimensional version ...
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2005-08-08BuchStability 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 ...
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2005-02-25BuchStochastic integer programming We consider empirical approximations of two-stage stochastic mixed-integer programs and derive central limit theorems for the objectives and optimal values. The limit theorems are based on empirical process theory and the ...
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2005-01-12BuchStress 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 ...
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2005-06-21BuchStructural 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 ...
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2005-07-06BuchThe value of multi-stage 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, ...
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2005-03-11BuchTwo-stage stochastic semidefinite programming and decomposition based interior point methods We 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 ...
