Convex Optimal Uncertainty Quantification
Optimization and Control
2015-04-29 v2
Abstract
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.
Cite
@article{arxiv.1311.7130,
title = {Convex Optimal Uncertainty Quantification},
author = {Shuo Han and Molei Tao and Ufuk Topcu and Houman Owhadi and Richard M. Murray},
journal= {arXiv preprint arXiv:1311.7130},
year = {2015}
}
Comments
Accepted for publication in SIAM Journal on Optimization