Skip to main content
SpringerLink
Log in

Conditions of solvability of vector problems using linear convolution of criteria

  • Published:
Cybernetics and Systems Analysis Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. V. S. Mikhalevich and V. L. Volkovich, Computing Methods of the Investigation and Design of Complex Systems [in Russian], Nauka, Moscow (1982).

    Google Scholar 

  2. V. V. Podinovskii and V. D. Nogin, Pareto-Optimal Solutions of Multicriteria Problems [in Russian], Nauka, Moscow (1982).

    Google Scholar 

  3. R. Steuer, Multicriteria Optimization, Wiley, New York (1985).

    Google Scholar 

  4. Yu. A. Dubov, S. I. Travkin, and V. N. Yakimets, Multicriteria Models of Formation and Selection of Variants of Systems [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  5. A. M. Geoffrion, “Proper efficiency and the theory of vector maximization,” J. Math. Anal. Appl., No. 22, 618-630 (1968).

    Google Scholar 

  6. V. A. Yemelichev and V. A. Perepelitsa, “Complexity of discrete multicriteria problems,” Diskret. Mat.,1, No. 6, 3–33 (1994).

    Google Scholar 

  7. V. A. Yemelichev and M. K. Kravtsov, “On unsolvability of vector problems of discrete optimization on systems of subsets in the class of algorithms of linear convolution of criteria,” Dokl. Ross. Akad. Nauk,334, No. 1, 9–11 (1994).

    Google Scholar 

  8. V. A. Yemelichev and M. K. Kravtsov, “On problems of discrete vector optimization on systems of subsets that are unsolvable using algorithms of linear convolution,” Zh. Vychisl. Mat. Mat. Fiz.,34, No. 7, 1082–1094 (1994).

    Google Scholar 

  9. V. A. Yemelichev, M. K. Kravtsov, and O. A. Yanushkevich, “Optimality conditions in one discrete vector problem on systems of subsets,” Zh. Vychisl. Mat. Mat. Fiz.,35, No. 11, 1641–1652 (1995).

    Google Scholar 

  10. V. A. Perepelitsa and I. V. Sergienko, “Investigation of one class of integer multicriteria problems,” Zh. Vychisl. Mat. Mat. Fiz.,28, No. 3, 400–419 (1988).

    MATH  Google Scholar 

  11. V. A. Yemelichev, M. K. Kravtsov, and O. A. Yanushkevich, “Lexicographic optima of a multicriteria problem of discrete optimization,” Mat. Zametki,3, No. 58, 365–371 (1995).

    Google Scholar 

  12. E. Girlich, V. A. Yemelichev, and O. A. Janushkevich, “Lexikographische Optima für Vektoroptimierungs-probleme,” Prepr. Otto-von-Göericke Univ. Magdeburg, No. 24 (1995).

  13. R. E. Burkard, H. Keiding, J. Krarup, and P. M. Pruzan, “A relationship between optimality and efficiency in multicriteria 0–1 programming problems,” Comput. Oper. Res.,8, No. 4, 241–247 (1981).

    Article  Google Scholar 

  14. M. K. Kravtsov and O. A. Yanushkevich, “On multicriteria problems solvable using the algorithm of linear convolution of criteria,” Prepr. AN Belarusi, Inst. Tekh. Kibern., Minsk, No. 16 (1995).

    Google Scholar 

  15. A. A. Gladkii and O. A. Yanushkevich, “On linear convolution of partial criteria of vector minimization problems,” in: Abstracts of Papers of the 9th All-Russian Conference on Mathematical Programming and Applications [in Russian], Ekaterinburg (1995).

  16. I. I. Melamed and I. H. Sigal, “Study of linear convolution of criteria in multicriteria discrete programming,” Zh. Vychisl. Mat. Mat. Fiz.,35, No. 8, 1260–1270 (1995).

    Google Scholar 

  17. V. A. Yemelichev, M. M. Kovalyov, and M. K. Kravtsov, Polyhedrons, Graphs, and Optimization [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  18. I. V. Sergienko, Mathematical Models and Methods of Solving Discrete Optimization Problems [in Russian], Naukova Dumka, Kiev (1988).

    Google Scholar 

  19. H. Papadimitriu and K. Steiglitz, Combinatorial Optimization, Algorithms, and Complexity [Russian translation], Mir, Moscow (1985).

    Google Scholar 

  20. V. K. Leont’yev and E. N. Gordeev, “Qualitative examination of trajectory problems,” Kibernetika, No. 5, 82–89 (1986).

  21. V. A. Yemelichev and M. K. Kravtsov, “On combinatorial problems of vector optimization,” Diskret. Mat.,1, No. 7, 3–18 (1995).

    Google Scholar 

  22. V. A. Yemelichev, M. K. Kravtsov, and O. A. Yanushkevich, “On solvability of vector problems on systems of subsets using a linear criteria convolution algorithm,” Abstracts of papers of the Second Intern. Conf. “Mathematical Algorithms” [in Russian], Nizhny Novgorod (1995).

  23. V. A. Yemelichev, M. K. Kravtsov, and O. A. Yanushkevich, “Solvability of minimax problems of vector optimization using an algorithm of linear convolution of criteria,” in: Abstracts of Papers of the 9th All-Russian Conference “Mathematical Programming and Applications” [in Russian], Ekaterinburg (1995).

Download references

Authors
  1. É. Girlikh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. M. Kovalyov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. K. Kravtsov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. O. A. Yanushkevich
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Kibemetika i Sistemnyi Analiz, No. 1, pp. 81–95, January–February, 1999.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Girlikh, É., Kovalyov, M.M., Kravtsov, M.K. et al. Conditions of solvability of vector problems using linear convolution of criteria. Cybern Syst Anal 35, 75–88 (1999). https://doi.org/10.1007/BF02667917

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02667917

Keywords

Search

Navigation