Geodesic
On scalarization of vector optimization type problems
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2012), pp. 8-18.

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We consider scalarization issues for vector problems in the case when the preference relation is represented by a rather arbitrary set. We propose an algorithm for weights choice for a priori unknown preference relations. We give some examples of applications to vector optimization problems, game equilibrium ones, and to variational inequalities.
Keywords: vector problems, scalarization, algorithm for weights choice. 
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I. V. Konnov. On scalarization of vector optimization type problems. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2012), pp. 8-18. http://geodesic.mathdoc.fr/item/IVM_2012_9_a1/

[1] N. N. Moiseev (red.), Sovremennoe sostoyanie teorii issledovaniya operatsii, Nauka, M., 1979 | MR

[2] Podinovskii V. V., Nogin V. D., Pareto-optimalnye resheniya mnogokriterialnykh zadach, Nauka, M., 1982 | MR

[3] Sawaragi Y., Nakayama H., Tanino T., Theory of multiobjective optimization, Academic Press, New York, 1985 | MR | Zbl

[4] Chen G. Y., Huang X. X., Yang X. Q., Vector optimization, Springer, Berlin, 2005 | MR

[5] Pshenichnyi B. N., Vypuklyi analiz i ekstremalnye zadachi, Nauka, M., 1980 | MR | Zbl

[6] Demyanov V. F., Vasilev L. V., Nedifferentsiruemaya optimizatsiya, Nauka, M., 1981 | MR

[7] Konnov I. V., Khabibullin R. F., “Algoritm otyskaniya elementa iz sopryazhennogo konusa”, Issled. po prikl. matem., 11, Part 1, Kazan, 1984, 32–40 | MR

[8] Barvinok A., A course in convexity, AMS, Providence, 2002 | Zbl

[9] Isac G., Bulavsky V. A., Kalashnikov V. V., Complementarity, equilibrium, efficiency and economics, Kluwer, Dordrecht, 2002 | MR | Zbl

[10] Gurvits L., “Programmirovanie v lineinykh prostranstvakh”: Errou K. Dzh., Gurvits L., Udzava Kh., Issledovaniya po lineinomu i nelineinomu programmirovaniyu, In. lit., M., 1962, 65–155

[11] Luc D. T., Theory of vector optimization, Springer, Berlin, 1989 | MR

[12] Nogin V. D., Prinyatie reshenii v mnogokriterialnoi srede, Fizmatlit, M., 2002 | Zbl

[13] Podinovskii V. V., “Aksiomaticheskoe reshenie problemy vazhnosti kriteriev v mnogokriterialnykh zadachakh”, Sovremennoe sostoyanie teorii issledovaniya operatsii, Nauka, M., 1979, 117–149 | MR

[14] Farquharson R., “Sur une généralisation de la notion d' équilibrium”, Compt. Rend. Acad. Sci. Paris, 240 (1955), 46–48 | MR | Zbl

[15] Blackwell D., “An analogue of the minimax theorem for vector payoffs”, Pacific J. Math., 6:1 (1956), 1–8 | MR | Zbl

[16] Konnov I. V., “Kombinirovannyi relaksatsionnyi metod dlya poiska vektornogo ravnovesiya”, Izv. vuzov. Matem., 1995, no. 12, 54–62 | MR | Zbl

[17] Nikaidô H., Isoda K., “Note on noncooperative convex games”, Pacific J. Math., 5, Suppl. 1 (1955), 807–815 | MR

[18] Konnov I. V., “Generalized monotone equilibrium problems and variational inequalities”, Handbook of Generalized Convexity and Generalized Monotonicity, chap. 13, eds. N. Hadjisavvas, S. Komlósi, S. Schaible, Springer, New York, 2005, 559–618 | DOI | MR | Zbl

[19] F. Giannessi (Ed.), Vector variational inequalities and vector equilibria. Mathematical theories, Kluwer Academic Publishers, Dordrecht–Boston–London, 2000 | MR