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Convex Optimal Uncertainty Quantification

Han, Shuo and Tao, Molei and Topcu, Ufuk and Owhadi, Houman and Murray, Richard M. (2015) Convex Optimal Uncertainty Quantification. SIAM Journal of Optimization, 25 (3). pp. 1368-1387. ISSN 1052-6234. https://resolver.caltech.edu/CaltechAUTHORS:20151030-084615377

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1137/13094712XDOIArticle
http://epubs.siam.org/doi/abs/10.1137/13094712XPublisherArticle
http://arxiv.org/abs/1311.7130arXivDiscussion Paper
ORCID:
AuthorORCID
Owhadi, Houman0000-0002-5677-1600
Murray, Richard M.0000-0002-5785-7481
Additional Information:© 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.
Funders:
Funding AgencyGrant Number
NSFCNS-0931746
Air Force Office of Scientific Research (AFOSR)FA9550-12-1-0389
Subject Keywords:convex optimization, uncertainty quantification, duality theory
Issue or Number:3
Classification Code:AMS subject classifications. 90C25, 90C46, 90C15, 60-08
Record Number:CaltechAUTHORS:20151030-084615377
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20151030-084615377
Official Citation:Convex Optimal Uncertainty Quantification Shuo Han, Molei Tao, Ufuk Topcu, Houman Owhadi, and Richard M. Murray SIAM Journal on Optimization 2015 25:3, 1368-1387
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:61734
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:03 Nov 2015 00:54
Last Modified:03 Oct 2019 09:11

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