Institut für Mathematik
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20170419BuchQuantitative Stability Analysis for Minimax Distributionally Robust RiskOptimization This paper considers distributionally robust formulations of a two stage stochastic programming problem with the objective of minimizing a distortion risk of the minimal cost incurred at the second stage.We carry out ...

20170419BuchOptimal scenario generation and reduction in stochastic programming Scenarios are indispensable ingredients for the numerical solution of stochastic optimization problems. Earlier approaches for optimal scenario generation and reduction are based on stability arguments involving distances ...

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

20160905BuchUniformly monotone functions  defiitions, properties, characterizations Quasiconcave functions play an important role in economics and finance as utility functions, measures of risk or other objects used, mainly, in portfolio selection analysis. A special attention is paid to these functions ...

20151005BuchClustering of sample average approximation for stochastic program We present an improvement to the Sample Average Approximation (SAA) method for twostage stochastic program. Although the SAA has nice theoretical properties, such as convergence in probability and consistency, as long ...

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

20151016BuchParallel stochastic optimization based on descent algorithms This study addresses the stochastic optimization of a function unknown in closed form which can only be estimated based on measurements or simulations. We consider parallel implementations of a class of stochastic ...

20150914BuchConvergence of the Smoothed Empirical Process in Nested Distance The nested distance, also process distance, provides a quantitative measure of distance for stochastic processes. It is the crucial and determining distance for stochastic optimization problems. In this paper we ...

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

20150422BuchA Comment on "Computational Complexityof Stochastic Programming Problems" Although stochastic programming problems were always believed to be computationally chal lenging, this perception has only recently received a theoretical justification by the seminal work of Dyer and Stougie (Mathematical ...

20150409BuchA Simulation Based Approach to Solve A Specific Type of Chance Constrained Optimization We solve the chance constrained optimization with convex feasible set through approximating the chance constraint by another convex smooth function. The approximation is based on the numerical properties of the Bernstein ...

20141230BuchQuasiMonte Carlo methods for linear twostage stochastic programming problems QuasiMonte Carlo algorithms are studied for generating scenarios to solve twostage linear stochastic programming problems. Their integrands are piecewise linearquadratic, but do not belong to the function spaces considered ...

20141230BuchDistribution shaping and scenario bundling for stochastic programs with endogenous uncertainty Stochastic programs are usually formulated with probability distributions that are exogenously given. Modeling and solving problems with endogenous uncertainty, where decisions can influence the probabilities, has remained ...

20141016BuchDynamic Generation of Scenario Trees We present new algorithms for the dynamic generation of scenario trees for multistage stochastic optimization. The different methods described are based on random vectors, which are drawn from conditional distributions ...

20140507BuchOn Distributionally Robust Multiperiod Stochastic Optimization This paper considers model uncertainty for multistage stochastic programs. The data and information structure of the baseline model is a tree, on which the decision problem is defined. We consider ambiguity neighborhoods ...

20140416BuchMitigating Uncertainty via Compromise Decisions in Twostage Stochastic Linear Programming Stochastic Programming (SP) has long been considered as a welljustified yet computationally challenging paradigm for practical applications. Computational studies in the literature often involve approximating a large ...

20140404BuchMultiObjective Probabilistically Constrained Programming with Variable Risk: New Models and Applications We consider a class of multiobjective probabilistically constrained problems MOPCP with a joint chance constraint, a multirow random technology matrix, and a risk parameter (i.e., the reliability level) defined as a ...

20130917BuchAncestral Benders' Cuts and Multiterm Disjunctions for MixedInteger Recourse Decisions in Stochastic Programming This paper focuses on solving twostage stochastic mixed integer programs (SMIPs) with general mixed integer decision variables in both stages. We develop a decomposition algorithm in which the first stage approximation ...

20130725BuchConditioning of linearquadratic twostage stochastic optimization problems In this paper a condition number for linearquadratic twostage stochastic optimization problems is introduced as the Lipschitz modulus of the multifunction assigning to a (discrete) probability distribution the solution ...

20130724BuchBidding in sequential electricity markets: The Nordic case For electricity market participants trading in sequential markets with differences in price levels and risk exposure, coordinated bidding is highly relevant. We consider a Nordic power producer who engages in the dayahead ...