Paper Info
Title
Maximal inner boxes in parametric AE -solution sets with linear shape
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.
Year
DOI
Venue
2015
10.1016/j.amc.2015.08.003
Applied Mathematics and Computation
Keywords
Field
DocType
Linear equations,Dependent interval parameters,Tolerable solution set,AE-solution set,Inner estimation
Discrete mathematics,Linear equation,Linear independence,Mathematical optimization,Linear system,Polynomial,Mathematical analysis,Polyhedron,Parametric statistics,Solution set,Linear programming,Mathematics
Journal
Volume
ISSN
Citations 
270
0096-3003
2
PageRank 
References 
Authors
0.42
12
2
Name
Order
Citations
PageRank
Milan Hladík126836.33
Evgenija D. Popova26814.20