Testing weak optimality of a given solution in interval linear programming revisited: NP-hardness proof, algorithm and some polynomially-solvable cases

  • Miroslav Rada
  • Milan Hladík
  • Elif Garajová
Original Paper


We address the problem of testing weak optimality of a given solution of a given interval linear program. The problem was recently wrongly stated to be polynomially solvable. We disprove it. We show that the problem is NP-hard in general. We propose a new algorithm for the problem, based on orthant decomposition and solving linear systems. Running time of the algorithm is exponential in the number of equality constraints. In particular, the proposed algorithm runs in polynomial time for interval linear programs with no equality constraints.


Interval linear programming Weakly optimal solution Weak optimality testing 



The work of M. Rada was supported by the Czech Science Foundation Grant P403/17-13086S. The work of M. Hladík and E. Garajová was supported by the Czech Science Foundation Grant P403/18-04735S. The work of E. Garajová was also supported by Grant No. 156317 of Grant Agency of Charles University.


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Copyright information

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

Authors and Affiliations

  1. 1.Department of Financial Accounting and Auditing, Faculty of Finance and AccountingUniversity of EconomicsPragueCzech Republic
  2. 2.Department of Applied Mathematics, Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic

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