Invited Session Tue.2.MA 141

Tuesday, 13:15 - 14:45 h, Room: MA 141

Cluster 22: Stochastic optimization [...]

Stochastic optimization - Confidence sets, stability, robustness


Chair: Petr Lachout



Tuesday, 13:15 - 13:40 h, Room: MA 141, Talk 1

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.



Tuesday, 13:45 - 14:10 h, Room: MA 141, Talk 2

Petr Lachout
Local information in stochastic optimization program


Historical observations contain information about local structure of the considered system.
We can use them to built an local estimator of the probability distribution leading the system.
Another local information is also available as
expert suggestions and forecasts,
knowledge about density smoothness, etc.
We intend to describe structure of such optimization programs together with a stability discussion.



Tuesday, 14:15 - 14:40 h, Room: MA 141, Talk 3

Milos Kopa
Robustness in stochastic programs with risk and probabilistic constraints

Coauthor: Jitka Dupacova


The paper presents robustness results for stochastic programs with risk, stochastic dominance and probabilistic constraints. Due to their frequently observed lack of convexity and/or smoothness, these programs are rather demanding both from the computational and robustness point of view. Under suitable conditions on the structure of the problem, we exploit the contamination technique to analyze the resistance of optimal value with respect to the alternative probability distribution.
We apply this approach to mean-risk models and portfolio efficiency testing with respect to stochastic dominance criteria.


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