Robust Solutions for Systems of Uncertain Linear Equations

Jianzhe Zhen, Dick den Hertog

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Abstract

Our contribution is twofold. Firstly, for a system of uncertain linear equations where the uncertainties are column-wise and reside in general convex sets, we show that the intersection of the set of possible solutions and any orthant is convex. We derive a convex representation of this intersection to calculate the ranges of the coordinates. Secondly, we propose two new methods for obtaining robust solutions of systems of uncertain linear equations. The first method calculates the center of the maximum inscribed ellipsoid of the set of possible solutions. The second method minimizes the expected violations with respect to the worst-case distribution. We compare these two new methods both theoretically and numerically with an existing method. The existing method minimizes the worst-case violation. Applications to the input-output model, Colley's Matrix Rankings and Article Influence Scores demonstrate the advantages of the two new methods.
Original languageEnglish
Place of PublicationTilburg
PublisherCentER, Center for Economic Research
Number of pages33
Volume2015-044
Publication statusUnpublished - 26 Aug 2015

Publication series

NameCentER Discussion Paper
Volume2015-044

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Keywords

  • interval linear systems
  • uncertain linear equations
  • maximum volune inscribed ellipsoid
  • worst-case distribution
  • robust least-squares
  • input-output model
  • Colley's Matrix Rankings
  • article influence scores

Cite this

Zhen, J., & den Hertog, D. (2015). Robust Solutions for Systems of Uncertain Linear Equations. (CentER Discussion Paper; Vol. 2015-044). Tilburg: CentER, Center for Economic Research.