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20000829BuchA note on the connectedness of chance constraints Henrion, RenéWe prove a result on connectedness of (functional) chance constraints $ P(h(x) \ge g(\xi) \ge p$, where the decision variable $x$ belongs to a Banach space and $h$ is assumed to be strictly quasiconcave. The derived ...

20051026BuchCharacterization of stability for cone increasing constraint mappings Henrion, RenéWe investigate stability (in terms of metric regularity) for the specific class of cone increasing constraint mappings. This class is of interest in problems with additional knowledge on some nondecreasing behavior of the ...

20060515BuchConvexity of chance constraints with independent random variables Henrion, René; Strugarek, CyrilleWe investigate the convexity of chance constraints with independent random variables. It will be shown, how concavity properties of the mapping related to the decision vector have to be combined with a suitable property ...

20030306BuchHölder and Lipschitz Stability of Solution Sets in Programs with Probabilistic Constraints Henrion, René; Römisch, WernerWe study perturbations of a stochastic program with a probabilistic constraint and $r$concave original probability distribution. First we improve our earlier results substantially and provide conditions implying Hölder ...

20201110ZeitschriftenartikelJoint Model of ProbabilisticRobust (Probust) Constraints Applied to Gas Network Optimization Adelhütte, Dennis; Aßmann, Denis; González Grandón, Tatiana; Gugat, Martin; Heitsch, Holger; Henrion, René; Liers, Frauke; Nitsche, Sabrina; Schultz, Rüdiger; Stingl, Michael; Wintergerst, DavidOptimization problems under uncertain conditions abound in many reallife applications. While solution approaches for probabilistic constraints are often developed in case the uncertainties can be assumed to follow a certain ...

20050426BuchLipschitz and differentiability properties of quasiconcave and singular normal distribution functions Henrion, René; Römisch, WernerThe 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 ...

20051021BuchMetric regularity and quantitative stability in stochastic programs with probabilistic constraints Henrion, René; Römisch, WernerNecessary and sufficient conditions for metric regularity of (several joint) probabilistic constraints are derived using recent results from nonsmooth analysis. The conditions apply to fairly general nonconvex, nonsmooth ...

20030210BuchPerturbation ananlysis of chanceconstrained programs under variation of all constraint data Henrion, RenéA fairly general shape of chance constraint programs is\[(P) min \{ g(x)  x \in X, \mu (H(x)) \le p \} ,\]where $g : \R^m \to \R$ is a continuous objective function, $X \subseteq \R^m$ is a closed subset of deterministic ...

20040605BuchPolyhedral inclusionexclusion Bukszar, Jozsef; Henrion, René; Hujter, Mihaly; Szantai, TamasMotivated 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 ...

20061026BuchScenario reduction in stochastic programming with respect to discrepancy distances Henrion, René; Küchler, Christian; Römisch, WernerDiscrete approximations to chance constrained and mixedinteger twostage stochastic programs require moderately sized scenario sets. The relevant distances of (multivariate) probability distributions for deriving quantitative ...

20061027BuchSome remarks on valueatrisk optimization Henrion, RenéWe discuss two observations related to valueatarisk optimization. First we consider a portfolio problem under an infinite number of valueatrisk inequality constraints (modelling first order stochastic dominance). The ...

20050621BuchStructural Properties of Linear Probabilistic Constraints Henrion, RenéThe 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 ...

20001102BuchStructure and stability of probabilistic storage level constraints Henrion, RenéWe consider the structure of probabilistic storage level constraints as well as the stability of solutions to optimization problems involving such constraints. Apart from the general case, special structures with and without ...

20051021BuchTopological Properties of the Approximate Subdifferential Henrion, RenéThe approximate subdifferential introduced by Mordukhovich has attracted much attention in recent works on nonsmooth optimization. Potential advantages over other concepts of subdifferentiability might be related to its ...