Volume 2004
Recent Submissions

20041227BuchOn the FortetMourier metric for the stability of Stochastic Optimization Problems, an example We consider the use of the FortetMourier metric between two probability measures to bound the error term made by an approximated solution of a stochastic program. After a short analysis of usual stability arguments, we ...

20041002BuchTwostage integer programs with stochastic righthand sides We consider twostage pure integer programs with discretely distributed stochastic righthand sides. We present an equivalent superadditive dual formulation that uses the value functions in both stages. We give two algorithms ...

20041002BuchA class of stochastic programs with decision dependent uncertainty The standard approach to formulating stochastic programs is based on the assumption that the stochastic process is independent of the optimization decision. We address a class of problems where the optimization decisions ...

20041002BuchVariance reduction in sample approximations of stochastic programs This paper studies the use of randomized QuasiMonte Carlo methods (RQMC) in sample approximations of stochastic programs. In high dimensional numerical integration, RQMC methods often substantially reduce the variance of ...

20040913BuchOn deviation measures in stochastic integer programming We propose extensions of traditional expectationbased stochastic integer programs to meanrisk models. Risk is measured by expected deviations of suitable random variables from their means or from preselected targets. We ...

20040913BuchConditional valueatrisk in stochastic programs with mixedinteger recourse In classical twostage stochastic programming the expected value of the total costs is minimized. Recently, meanrisk models  studied in mathematical finance for several decades  have attracted attention in stochastic ...

20040615BuchTreasury management model with foreign exchange exposure In this paper we formulate a model for foreign exchange exposure management and (international) cash management taking into consideration random fluctuations of exchange rates. A vector error correction model (VECM) is ...

20040605BuchPolyhedral inclusionexclusion Motivated by numerical computations to solve probabilistic constrained stochastic programming problems, we derive a new identity claiming that many terms are cancelled out in the inclusionexclusion formula expressing the ...

20040521BuchArbitrage pricing of American contingent claims in incomplete markets  a convex optimization approach Convex optimization provides a natural framework for pricing and hedging financial instruments in incomplete market models. Duality theory of convex optimization has been shown to yield elementary proofs of wellknown ...

20040517BuchA stochastic programming approach to resourceconstrained assignment problems We address the resourceconstrained generalizations of the assignment problem with uncertain resource capacities, where the resource capacities have an unknown distribution that can be sampled. We propose three stochastic ...

20040517BuchAssessing policy quality in multistage stochastic programming Solving a multistage stochastic program with a large number of scenarios and a moderatetolarge number of stages can be computationally challenging. We develop two Monte Carlobased methods that exploit special structures ...

20040420BuchDecompositionbased interior point methods for twostage stochastic convex quadratic programs with recourse Zhao [28] recently showed that the log barrier associated with the recourse function of twostage stochastic linear programs behaves as a strongly selfconcordant barrier and forms a self concordant family on the first ...

20040416BuchMeanrisk objectives in stochastic programming Traditional stochastic programming is risk neutral in the sense that it is concerned with the optimization of an expectation criterion. A common approach to addressing risk in decision making problems is to consider a ...

20040325BuchConditional Risk Mappings We introduce an axiomatic definition of a conditional convex risk mapping and we derive its properties. In particular, we prove a representation theorem for conditional risk mappings in terms of conditional expectations. ...

20040325BuchOptimization of Convex Risk Functions We consider optimization problems involving convex risk functions. By employing techniques of convex analysis and optimization theory in vector spaces of measurable functions we develop new representation theorems for risk ...

20040301BuchConvexification of stochastic ordering We consider sets defined by the usual stochastic ordering relation and by the second order stochastic dominance relation. Under fairy general assumptions we prove that in the space of integrable random variables the closed ...

20040221BuchA branchandcut algorithm for the stochastic uncapacitated lotsizing problem This paper addresses a multistage stochastic integer programming formulation of the uncapacitated lotsizing problem under uncertainty. We show that the classical $(\mathcal{l}, S)$ inequalities for the deterministic ...

20040219BuchA factor 1/2 approximation algorithm for a class of twostage stochastic mixedinteger programs Abstract We introduce the twostage stochastic maximumweight matching problem and demonstrate that this problem is NPcomplete. We give a factor 1/2 approximation algorithm and prove its correctness. We also provide a ...

20040219BuchThe millionvariable "march" for stochastic combinatorial optimization Combinatorial optimization problems have applications in a variety of sciences and engineering. In the presence of data uncertainty, these problems lead to stochastic combinatorial optimization problems which result in ...

20040210BuchEpiconvergent discretizations of multistage stochastic programs In many dynamic stochastic optimization problems in practice, the uncertain factors are best modeled as random variables with an infinite support. This results in infinitedimensional optimization problems that can rarely ...