Calculating the exact bounds of optimal values in LP with interval coefficients

Annals of Operations Research

Volumn 81, Issue , 1998, Pages 51-62

  Mráz, František ^a  

^a UNIVERSITY OF SOUTH BOHEMIA   (Czech Republic)

Author keywords

Inexact data; Interval coefficients; Linear programming problem

Indexed keywords

EID: 0043231081     PISSN: 02545330     EISSN: 15729338     Source Type: Journal    
DOI: 10.1023/a:1018985914065     Document Type: Article

References (16)

1. H. Beeck, Linear programming with inexact data, Report TUM-ISU-7830, Technical University, Munich, 1978.
2. C. Jansson, A self-validating method for solving linear programming problems with interval input data, Computing Suppl. 6(1988)33-46.
3. C. Jansson and S.M. Rump, Rigorous solution of linear programming problems with uncertain data, ZOR 35(1991)87-111.
4. R. Krawczyk, Fehlerabschätzung bei linearer Optimierung, in: Interval Mathematics, ed. K. Nickel, Springer, Berlin, 1975, pp. 215-222.
5. F. Mráz, Nonnegative solutions of interval linear systems, in: Computer Arithmetic and Enclosure Methods, eds. L. Atanassova and J. Herzberger, Elsevier, Amsterdam, 1992, pp. 299-308.
6. F. Mráz, On supremum of the solution function in linear programs with interval coefficients, KAM-Series No. 93-236, Dept. of Applied Math., Charles University, Prague, 1993, pp. 1-18.
7. F. Mráz, The algorithm for solving interval linear programs and comparison with similar approaches, KAM-Series No. 93-239, Dept. of Applied Math., Charles University, Prague, 1993, pp. 1-11.
8. F. Mráz and V. Kabele, Investigation of linear programs and their feasible solutions under uncertainty, Report Series 9, University of South Bohemia, Dept. of Math., 1993, pp. 71-82.
9. F. Mráz, On infimum of optimal objective function values in interval linear programming, KAM-Series No.96-337, Dept. of Applied Math., Charles University, Prague, 1996, pp. 1-16.
10. F. Mráz, The exact lower bound of optimal values in interval LP, in: Scientific Computing and Validated Numerics, eds. G. Alefeld, A. Frommer and B. Lang, Akademie Verlag, Berlin, 1996, pp. 214-220.
11. F. Nožička, J. Guddat and H. Hollatz, Theorie der linearen Optimierung, Springer, Berlin, 1972.
12. W. Oettli and W. Prager, Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides, Numerische Mathematik 6(1964)405-409.
13. J. Rohn, Duality in interval linear programming, in: Interval Mathematics, ed. K. Nickel, Academic Press, New York, 1980.
14. J. Rohn, Interval linear systems, Freiburger Intervall-Berichte 84/7(1984)33-58.
15. J. Rohn, Miscellaneous results on linear interval systems, Freiburger Intervall-Berichte 85/9(1985) 29-43 (1985).
16. J. Rohn, NP-hardness results for some linear and quadratic problems, Technical Report No. 619, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague, 1995, pp. 1-11.