Paper Info
Title
On probabilistic constraints induced by rectangular sets and multivariate normal distributions
Abstract
In this paper, we consider optimization problems under probabilistic constraints which are defined by two-sided inequalities for the underlying normally distributed random vector. As a main step for an algorithmic solution of such problems, we derive a derivative formula for (normal) probabilities of rectangles as functions of their lower or upper bounds. This formula allows to reduce the calculus of such derivatives to the calculus of (normal) probabilities of rectangles themselves thus generalizing a similar well-known statement for multivariate normal distribution functions. As an application, we consider a problem from water reservoir management. One of the outcomes of the problem solution is that the (still frequently encountered) use of simple individual probabilistic can completely fail. In contrast, the (more difficult) use of joint probabilistic constraints which heavily depends on the derivative formula mentioned before yields very reasonable and robust solutions over the whole time horizon considered.
Year
DOI
Venue
2010
10.1007/s00186-010-0316-3
Mathematical Methods of Operations Research
Keywords
Field
DocType
water reservoir management,derivative of probabilities of rectangles,stochastic programming,probabilistic constraints,stochastic programming · probabilistic constraints · chance constraints · derivative of probabilities of rectangles · water reservoir management,normal distribution,upper bound,multivariate normal distribution,optimization problem
Discrete mathematics,Mathematical optimization,Time horizon,Generalization,Multivariate normal distribution,Multivariate random variable,Probabilistic logic,Stochastic programming,Optimization problem,Mathematics
Journal
Volume
Issue
ISSN
71
3
1432-2994
Citations 
PageRank 
References 
14
1.51
3
Authors
4
Name
Order
Citations
PageRank
Wim Van Ackooij113112.33
René Henrion230529.65
Andris Möller3453.06
Riadh Zorgati4204.08