Spring 2016 Seminar Series

DATE: 5/5/16
LOCATION: E51-325
TIME: 4:15pm
Reception immediately following

SPEAKER:
Dick den Hertog

TITLE
Robust Counterparts of Ambiguous Stochastic Constraints Under Mean and Dispersion Information

ABSTRACT
We consider ambiguous stochastic constraints under partial information. Whereas the past literature used the variance as the dispersion measure, here we use the mean absolute deviation (MAD). This makes it possible to use the old result of Ben-Tal and Hochman (1972) in which tight upper and lower bounds on the expectation of a convex function of a random variable are given. We use these bounds to derive exact robust counterparts of expected feasibility of convex constraints and to construct new safe tractable approximations of chance constraints. Numerical examples show our method to be applicable to numerous applications of Robust Optimization, e.g., where implementation error or linear decision rules are present. Also, we show that the methodology can be used for optimization the average-case performance of worst-case optimal Robust Optimization solutions. These results are currently applied to Stochastic Programming problems where the optimal value of the optimization problems solved in later stages are convex functions of the uncertain parameters.

 

Joint work with Krzysztof Postek (TIlburg University), Aharon Ben-Tal (Technion), and Bertrand Melenberg (Tilburg University)