Convex Optimal Uncertainty Quantification
Optimal uncertainty quantification (OUQ) is a framework for numerical extreme-case analysis of stochastic systems with imperfect knowledge of the underlying probability distribution. This paper presents sufficient conditions under which an OUQ problem can be reformulated as a finite-dimensional convex optimization problem, for which efficient numerical solutions can be obtained. The sufficient conditions include that the objective function is piecewise concave and the constraints are piecewise convex. In particular, we show that piecewise concave objective functions may appear in applications where the objective is defined by the optimal value of a parameterized linear program.
© 2015, Society for Industrial and Applied Mathematics. Received by the editors December 2, 2013; accepted for publication (in revised form) April 21, 2015; published electronically July 14, 2015. This work was supported in part by NSF grant CNS-0931746 and AFOSR grant FA9550-12-1-0389.
Published - 13094712x.pdf
Submitted - 1311.7130v2.pdf