Joint dynamic probabilistic constraints with projected linear decision rules

TL;DR

This paper introduces a method for handling joint dynamic probabilistic constraints in multistage stochastic linear optimization by projecting decision rules onto hard constraints, with analytical computation of objectives and gradients.

Contribution

It develops a projection technique for decision rules onto hard constraints and analyzes the relation between original and approximating problems using linear decision rules.

Findings

Analytical computation of value and gradient functions for approximating problems.

Effective projection method for decision rules onto hard constraints.

Applicability to Gaussian and truncated Gaussian noise models.

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.