Maximal inner boxes in parametric AE-solution sets with linear shape

Milan Hladík and Evgenija D. Popova

Applied Mathematics and Computation, 2015, vol. 270, issue C, 606-619

Abstract: We consider linear systems of equations A(p)x=b(p), where the parameters p are linearly dependent and come from prescribed boxes, and the sets of solutions (defined in various ways) which have linear boundary. One fundamental problem is to compute a box being inside a parametric solution set. We first consider parametric tolerable solution sets (being convex polyhedrons). For such solution sets we prove that finding a maximal inner box is an NP-hard problem. This justifies our exponential linear programming methods for computing maximal inner boxes. We also propose a polynomial heuristic that yields a large, but not necessarily the maximal, inner box. Next, we discuss how to apply the presented linear programming methods for finding large inner estimations of general parametric AE-solution sets with linear shape. Numerical examples illustrate the properties of the methods and their application.

Keywords: Linear equations; Dependent interval parameters; Tolerable solution set; AE-solution set; Inner estimation (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:270:y:2015:i:c:p:606-619

DOI: 10.1016/j.amc.2015.08.003

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