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Original Articles

Farkas-type theorems for interval linear systems

, &
Pages 1390-1400 | Received 21 May 2014, Accepted 23 Jun 2014, Published online: 24 Jul 2014

References

  • Farkas J. Theorie der einfachen Ungleichungen [Theory of simple inequalities]. J. Reine. Angew. Math. 1902;124:1–27.
  • Rohn J. A Farkas-type theorem for linear interval equations. Computing. 1989;43:93–95.
  • Rohn J. A Farkas-type theorem for interval linear inequalities. Optim. Lett. 2014;8:1591–1598.
  • Rohn J. Linear programming with inexact data is NP-hard. Zeitsch. Angew. Math. Mech. 1998;78:S1051–S1052.
  • Karademir S, Prokopyev OA. A short note on solvability of systems of interval linear equations. Linear Multilinear Algebra. 2011;59:707–710.
  • Rohn J. Letter to the editor. Linear Multilinear Algebra. 2013;61:697–698.
  • Rohn J. A manual of results on interval linear problems. Technical Report 1164. Prague: Institute of Computer Science, Academy of Sciences of the Czech Republic; 2012. Available from: http://uivtx.cs.cas.cz/rohn/publist/manual.pdf
  • Fiedler M, Nedoma J, Ramík J, Rohn J, Zimmermann K. Linear optimization problems with inexact data. New York (NY): Springer-Verlag; 2006.
  • Rohn J. Solvability of systems of interval linear equations and inequalities. In: Fiedler M, Nedoma J, Ramík J, Rohn J, Zimmermann K,editors. Linear optimization problems with inexact data. New York (NY): Springer; 2006. p. 35–77.
  • Shary SP. Controllable solution set to interval static systems. Math. Comput. Simulation. 1997;86:185–196.
  • Shary SP. A new technique in systems analysis under interval uncertainty and ambiguity. Reliab. Comput. 2002;8:321–418.
  • Popova ED. Explicit description of AE solution sets for parametric linear systems. SIAM J. Matrix Anal. Appl. 2012;33:1172–1189.
  • Popova ED, Hladík M. Outer enclosures to the parametric AE solution set. Soft Comput. 2013;17:1403–1414.
  • Li W, Wang H, Wang Q. Localized solutions to interval linear equations. J. Comput. Appl. Math. 2013;238:29–38.
  • Allahdadi M, Nehi HM. The optimal solution set of the interval linear programming problems. Optim. Lett. 2013;7:1893–1911.
  • Hladík M. How to determine basis stability in interval linear programming. Optim. Lett. 2014;8:375–389.
  • Hladík M. On approximation of the best case optimal value in interval linear programming. Optim. Lett. 2014. doi:10.1007/s11590-013-0715-5.
  • Li W, Luo J, Deng C. Necessary and sufficient conditions of some strong optimal solutions to the interval linear programming. Linear Algebra Appl. 2013;439:3241–3255.
  • Li W, Luo J, Wang Q, Li Y. Checking weak optimality of the solution to linear programming with interval right-hand side. Optim. Lett. 2014;8:1287–1299.

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