Please use this identifier to cite or link to this item:
|Title:||Optimization under probabilistic envelope constraints|
|Authors:||Xu, H. |
|Citation:||Xu, H., Caramanis, C., Mannor, S. (2012-05). Optimization under probabilistic envelope constraints. Operations Research 60 (3) : 682-699. ScholarBank@NUS Repository. https://doi.org/10.1287/opre.1120.1054|
|Abstract:||Chance constraints are an important modeling tool in stochastic optimization, providing probabilistic guarantees that a solution "succeeds" in satisfying a given constraint. Although they control the probability of "success," they provide no control whatsoever in the event of a "failure." That is, they do not distinguish between a slight overshoot or undershoot of the bounds and more catastrophic violation. In short, they do not capture the magnitude of violation of the bounds. This paper addresses precisely this topic, focusing on linear constraints and ellipsoidal (Gaussian-like) uncertainties. We show that the problem of requiring different probabilistic guarantees at each level of constraint violation can be reformulated as a semi-infinite optimization problem. We provide conditions that guarantee polynomial-time solvability of the resulting semi-infinite formulation. We show further that this resulting problem is what has been called a comprehensive robust optimization problem in the literature. As a byproduct, we provide tight probabilistic bounds for comprehensive robust optimization. Thus, analogously to the connection between chance constraints and robust optimization, we provide a broader connection between probabilistic envelope constraints and comprehensive robust optimization. © 2012 INFORMS.|
|Source Title:||Operations Research|
|Appears in Collections:||Staff Publications|
Show full item record
Files in This Item:
There are no files associated with this item.
checked on Oct 12, 2018
WEB OF SCIENCETM
checked on Sep 26, 2018
checked on Jul 27, 2018
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.