Talk Abstract:

Efficient Points of Discrete Distributions in Probabilistic Optimization Models

Andrzej Ruszczynski
Department of Management Science and Information System
Rutgers University
rusz@rutcor.rutgers.edu

Joint work with Darinka Dentcheva and Andras Prekopa.

Stochastic optimization models with probabilistic constraints arise in manifold applications, in particular in environmental and energy models. We consider problems involving discrete random variables. The concept of $p$-efficient points of a probability distribution will be introduced and used to derive various equivalent problem formulations. Next we modify the concept of r-concave discrete probability distributions and analyse its relevance for problems under consideration. These notions are used to derive new lower and upper bounds for the optimal value of probabilistically constrained stochastic programming problems with discrete random variables. A number of new solution approaches based on these ideas will be presented and compared.

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