Monday, 16:15 - 16:40 h, Room: MA 141


Gabor Rudolf
Optimization with multivariate conditional-value-at-risk constraints

Coauthor: Nilay Noyan


For decision making problems under uncertainty it is crucial to specify the decision makers' risk preferences based on multiple stochastic performance measures. Incorporating multivariate preference rules into optimization models is a recent research area. Existing studies focus on extending univariate stochastic dominance rules to the multivariate case. However, enforcing such dominance constraints can be overly conservative in practice. As an alternative, we focus on the risk measure conditional value-at-risk (CVaR), introduce a multivariate CVaR relation, and propose an optimization model with multivariate CVaR constraints based on polyhedral scalarization. For finite probability spaces we develop a cut generation algorithm, where each cut is obtained by solving a mixed integer problem. We show that a multivariate CVaR constraint reduces to finitely many univariate CVaR constraints, which proves the finite convergence of our algorithm. We also show that our results can be extended to the wider class of coherent risk measures. The proposed approach provides a novel, flexible, and computationally tractable way of modeling preferences in stochastic multi-criteria decision making.


Talk 3 of the invited session Mon.3.MA 141
"Solution methods for constrained stochastic optimization" [...]
Cluster 22
"Stochastic optimization" [...]


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