Solving interval linear programming problems with equality constraints using extended interval enclosure solutions

  • Maryam Mohaghegh Tabar
  • Mohammad Keyanpour
  • Weldon A. LodwickEmail author
Methodologies and Application


This paper focuses on solving systems of interval linear equations and interval linear programming in a computationally efficient way. Since the computational complexity of most interval enclosure numerical methods is often prohibitive, a procedure to obtain a relaxation of the interval enclosure solution that is computationally tractable is proposed. We show that our approach unifies the four standard interval solutions—the weak, strong, control and tolerance solutions. The interval linear system methods require \(n\cdot 2^{n}\) linear solutions. However, in the case of linear programming problems, we show that this requires just two optimization problem of the size of the problem itself. Numerical examples illustrate our results.


Interval linear system Interval linear programming Constraint intervals Extended interval enclosure solutions 



The authors would like to thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper. The third author wishes to thank CNPq project #400754/2014-2 for partially supporting this research.

Compliance with ethical standards

Conflict of interest

The authors declared that they have no conflict of interest.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of SciencesUniversity of GuilanRashtIran
  2. 2.Department of MathematicsUniversity of Colorado DenverDenverUSA

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