Joint dynamic probabilistic constraints with projected linear decision rules. (3rd September 2017)

• Record Type: Journal Article
• Authors: Guigues, V.; Henrion, R.
• Is Part Of: Optimization methods and software. Volume 32:Number 5(2017)
• Page Start: 1006
• Page End: 1032
• Publication Date: 2017-09-03
• Subjects: dynamic probabilistic constraints -- multistage stochastic linear programs -- linear decision rules; 90C15 -- 90C90 -- 90C30; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2016.1233972
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : We consider multistage stochastic linear optimization problems combining joint dynamic probabilistic constraints with hard constraints. We develop a method for projecting decision rules onto hard constraints of wait-and-see type. We establish the relation between the original (infinite-dimensional) problem and approximating problems working with projections from different subclasses of decision policies. Considering the subclass of linear decision rules and a generalized linear model for the underlying stochastic process with noises that are Gaussian or truncated Gaussian, we show that the value and gradient of the objective and constraint functions of the approximating problems can be computed analytically.