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Convex Optimal Uncertainty Quantification

Authors
  • Han, Shuo
  • Tao, Molei
  • Topcu, Ufuk
  • Owhadi, Houman
  • Murray, Richard M.
Type
Preprint
Publication Date
Apr 27, 2015
Submission Date
Nov 27, 2013
Identifiers
arXiv ID: 1311.7130
Source
arXiv
License
Yellow
External links

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.

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