Tuesday, 13:15 - 13:40 h, Room: MA 141


Silvia Vogel
Confidence regions for level sets: Sufficient conditions


Real-life decision problems usually contain uncertainties. If a probability distribution of the uncertain quantities is available, the successful models of stochastic programming can be utilized. The probability distribution is usually obtained via estimation, and hence there is the need to judge the goodness of the solution of the `estimated' problem. Confidence regions for constraint sets, optimal values and solution sets of optimization problems provide useful information. Recently a method has been developed which offers the possibility to derive confidence sets employing a quantified version of convergence in probability of random sets instead of the whole distribution of a suitable statistic. Uniform concentration-of-measure inequalities for approximations of the constraint and/or objective functions are crucial conditions for the approach. We will discuss several methods for the derivation of such inequalities, especially for functions which are expectations of a random function.


Talk 1 of the invited session Tue.2.MA 141
"Stochastic optimization - Confidence sets, stability, robustness" [...]
Cluster 22
"Stochastic optimization" [...]


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