Centered Solutions for Uncertain Linear Equations

CentER Discussion Paper Series No. 2016-048

26 Pages Posted: 27 Aug 2015 Last revised: 22 Dec 2016

See all articles by Jianzhe Zhen

Jianzhe Zhen

Tilburg University - Center for Economic Research (CentER)

Dick den Hertog

Tilburg University - Department of Econometrics & Operations Research

Date Written: December 22, 2016

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. Secondly, to obtain centered solutions for systems of uncertain linear equations, we compute the maximum size inscribed convex body (MCB) of the set of all possible solutions. The obtained MCB is an inner approximation of the solution set, and its center is a potential solution to the system. We compare our method both theoretically and numerically with an existing method that minimizes the worst-case violation. Applications to the input-output model, Colley's Matrix Rankings and Article Influence Scores demonstrate the advantages of the new method.

Keywords: Interval linear systems; uncertain linear equations; maximum volume inscribed ellipsoid

JEL Classification: C61

Suggested Citation

Zhen, Jianzhe and den Hertog, Dick, Centered Solutions for Uncertain Linear Equations (December 22, 2016). CentER Discussion Paper Series No. 2016-048. Available at SSRN: https://ssrn.com/abstract=2651004 or http://dx.doi.org/10.2139/ssrn.2651004

Jianzhe Zhen (Contact Author)

Tilburg University - Center for Economic Research (CentER) ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Dick Den Hertog

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands

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