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@article{DM_2019_31_2_a2, author = {V. A. Emelichev and S. E. Bukhtoyarov}, title = {Investment {Boolean} problem with {Savage} risk criteria under uncertainty}, journal = {Diskretnaya Matematika}, pages = {20--33}, publisher = {mathdoc}, volume = {31}, number = {2}, year = {2019}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/DM_2019_31_2_a2/} }
V. A. Emelichev; S. E. Bukhtoyarov. Investment Boolean problem with Savage risk criteria under uncertainty. Diskretnaya Matematika, Tome 31 (2019) no. 2, pp. 20-33. http://geodesic.mathdoc.fr/item/DM_2019_31_2_a2/
[1] Markowitz H., “Portfolio selection”, J. Finance, 7:1 (1952), 77–91 | MR
[2] Sergienko I.V., Shilo V.P., Zadachi diskretnoi optimizatsii. Problemy, metody resheniya, issledovaniya, Naukova dumka, Kiev, 2003
[3] Sergienko I.V., Kozeratskaya L.N., Lebedeva T.T., Issledovanie ustoichivosti i parametricheskii analiz diskretnykh optimizatsionnykh zadach, Naukova dumka, Kiev, 1995
[4] Leontev V.K., “Diskretnaya optimizatsiya”, Zh. vychisl. matem. i matem. fiz., 47:2 (2007), 338–352 | MR | Zbl
[5] Gordeev E. N., “Comparison of three approaches to studying stability of solutions to problems of discrete optimization and computational geometry”, J. Applied and Industrial Mathematics, 9:3 (2015), 358–366 | DOI | MR | Zbl
[6] Emelichev V.A., Kotov V.M., Kuzmin K.G., Lebedeva T.T., Semenova N.V., Sergienko T.I., “Ustoichivost i effektivnye algoritmy resheniya zadach diskretnoi optimizatsii s mnogimi kriteriyami i nepolnoi informatsiei”, Problemy upravleniya i informatiki, 2014, no. 1, 53–67 | MR
[7] Emelichev V.A., Kuzmin K.G., Leonovich A.M., “Ustoichivost v vektornykh kombinatornykh zadachakh optimizatsii”, Avtomatika i telemekhanika, 2004, no. 2, 79–92 | Zbl
[8] Emelichev V. A., Gurevskij E. E., “On the stability kernel of a multicriteria combinatorial minimax problem”, J. Applied and Industrial Mathematics, 15:5 (2008), 6–19 | MR | Zbl
[9] Emelichev V.A., Kuzmin K.G., “O radiuse ustoichivosti vektornoi zadachi tselochislennogo lineinogo programmirovaniya v sluchae regulyarnosti normy v kriterialnom prostranstve”, Kibernetika i sistemnyi analiz, 2010, no. 1, 82–89 | MR | Zbl
[10] Emelichev V., Gurevsky E., Kuzmin K., “On stability of some lexicographic integer optimization problem”, Control and Cybernetics, 39:3 (2010), 811–826 | MR | Zbl
[11] Emelichev V., Karelkina O., Kuzmin K., “Qualitative stability analysis of multicriteria combinatorial minimum problems”, Control and Cybernetics, 41:1 (2012), 57–79 | MR | Zbl
[12] Gurevsky E., Battia O., Dolgui A., “Balancing of simple assembly lines under variations of task processing times”, Ann.Oper. Res., 2012, no. 201, 265–286 | DOI | MR | Zbl
[13] Lebedeva T.T., Semenova N.V., Sergienko T.I., “Ustoichivost vektornykh zadach tselochislennoi optimizatsii: vzaimosvyaz s ustoichivostyu mnozhestva optimalnykh i neoptimalnykh reshenii”, Kibernetika i sistemnyi analiz, 2005, no. 4, 90–100 | Zbl
[14] Lebedeva T.T., Sergienko T.I., “Raznye tipy ustoichivosti vektornoi zadachi tselochislennoi optimizatsii: obschii podkhod”, Kibernetika i sistemnyi analiz, 2008, no. 3, 142–148 | Zbl
[15] Libura M., van der Poort E., Sierksma G., van der Veen J., “Stability aspects of the travelling salesman problem based on $k$-best solutions”, Discrete Applied Mathematics, 87:1–3 (1998), 159–185 | DOI | MR | Zbl
[16] Leontev V.K., “Ustoichivost v lineinykh diskretnykh zadachakh”, Problemy kibernetiki, 35 (1979), 169–184, Moskva | Zbl
[17] Emelichev V.A., Podkopaev D.P., “Ustoichivost i regulyarizatsiya vektornykh zadach tselochislennogo lineinogo programmirovaniya”, Diskretnyi analiz i issledovanie operatsii. Ser.2, 8:1 (2001), 47–69 | MR | Zbl
[18] Emelichev V., Girlich E., Nikulin Yu., Podkopaev D., “Stability and regularization of vector problem of integer linear programming”, Optimization, 51:4 (2002), 645–676 | DOI | MR | Zbl
[19] Emelichev V. A., Kuzmin K. G., “On a type of stability of a multicriteria integer linear programming problem in the case of a monotone norm”, J. Comput. Syst. Sci. Int., 46:5 (2007), 714–720 | DOI | MR
[20] Emelichev V. A., Kuzmin K. G., “A general approach to studying the stability of a Pareto optimal solution of a vector integer linear programming problem”, Discrete Math. Appl., 17:4 (2007), 349–354 | DOI | DOI | MR | Zbl
[21] Emelichev V., Podkopaev D.P., “Quantitative stability analysis for vector problems of 0-1 programming”, Discrete Optimization, 7:1-2 (2010), 48–63 | DOI | MR | Zbl
[22] Emelichev V. A., Kuzmin K. G., “Estimating the stability radius of the vector MAX-CUT problem”, Discrete Math. Appl., 23:2 (2013), 145–152 | DOI | DOI | MR | Zbl
[23] Emelichev V.A., Kuzmin K.G., “O radiuse $T_1$-ustoichivosti mnogokriterialnoi lineinoi bulevoi zadachi s normami Geldera v prostranstvakh parametrov”, Tavricheskii vestnik matematiki i informatiki, 2016, no. 1, 49–64
[24] Chakravarti N., Wagelmans A., “Calculation of stability radius for combinatorial optimization problems”, Oper. Res. Lett., 23:1 (1998), 1–7 | DOI | MR | Zbl
[25] Van Hoesel S., Wagelmans A., “On the complexity of postoptimality analysis of 0-1 programs”, Discr. Appl. Math., 91:1–3 (1999), 251–263 | MR | Zbl
[26] Roland J., De Smet Y., Rui Figueira J., “On the calculation of stability radius for multi-objective combinatorial optimization problems by inverse optimization”, J. Oper. Res., 10:4 (2012), 379–389 | DOI | MR | Zbl
[27] Emelichev V. A., Korotkov V. V., Kuzmin K. G., “Multicriterial investment problem in conditions of uncertainty and risk”, J. Comput. Syst. Sci. Int., 50:6 (2011), 1011–1018 | DOI | MR | Zbl
[28] Emelichev V. A., Korotkov V. V., “On stability of a vector Boolean investment problem with Wald’s criteria”, Discrete Math. Appl., 22:4 (2012), 367–381 | DOI | DOI | MR | MR | Zbl
[29] Emelichev V. A., Korotkov V. V., “O radiuse ustoichivosti vektornoi investitsionnoi zadachi s kriteriyami minimaksnogo riska Sevidzha”, Kibernetika i sistemnyi analiz, 2012, no. 3, 68–77 | MR | Zbl
[30] Emelichev V., Korotkov V., Nikulin Yu., “Post-optimal analysis for Markowitz multicriterio portfolio optimization problem”, J. Multi-Criteria Decision Analysis, 21 (2014), 95–100 | DOI
[31] Emelichev V., Korotkov V., “On stability of multicriteria investment Boolean problem with Wald's efficiency criteria”, Bull. Acad. Sci. Moldova. Mathematics, 2014, no. 1(74), 3–13 | MR | Zbl
[32] Emelichev V.A., Ustilko E.V., “Postoptimalnyi analiz investitsionnoi zadachi s kriteriyami krainego optimizma”, Prikladnaya diskretnaya matematika, 2014, no. 3, 117–123
[33] Bukhtoyarov S.E., Emelichev V.A., “On the stability measure of solutions to a vector version of an investment problem”, Jour. Appl. Industr. Math., 9:3 (2015), 328–334 | DOI | MR | Zbl
[34] Emelichev V., Bukhtoyarov S., Mychkov V., “An investment problem under multicriteriality, uncertainty and risk”, Bull. Acad. Sci. Moldova. Mathematics, 2016, no. 3, 82–98 | MR | Zbl
[35] Sholomov L.A., Logicheskie metody issledovaniya diskretnykh modelei, Nauka, Moskva, 1989
[36] Yudin D.B., Vychislitelnye metody teorii prinyatiya reshenii, Nauka, Moskva, 1989
[37] Aizerman M.A., Alekserov F.T., Vybor variantov: osnovy teorii, Nauka, Moskva, 1990 | MR
[38] Lotov A.V., Pospelova I.I., Mnogokriterialnye zadachi prinyatiya reshenii, MAKS Press, Moskva, 2008
[39] Tepman L.N., Riski v ekonomike, YuNITI-DANA, Moskva, 2002
[40] Shapkin A.S., Ekonomicheskie i finansovye riski, Dashkov i Ko, Moskva, 2013
[41] Moskvin V.A., Riski investitsionnykh proektov, KURS: INFRA-M, Moskva, 2016
[42] Howell L. (ed.), Global risks 2013, World Economic Forum, Geneva, 2012
[43] Savage L. J., The foundations of statistics, Dover Publ., New York, 1972 | MR | Zbl
[44] Du D., Pardalos P. (eds.), Minimax and applications, Kluwer, Dordrecht, 1995 | MR | Zbl
[45] Demyanov V. F., Malozemov V. N., Vvedenie v minimaks, Nauka, Moskva, 1972 | MR
[46] Pareto V., Manuel d'economie politique, V. Giard E. Briere, Paris, 1909
[47] Slater M., Lagrange multipliers revisited: a contribution to nonlinear programming. Cowles Comission Discussion Paper No. 80: Mathematics 403, Cowles Foundation for Research in Economics, Yale University, 1950
[48] Podinovskii V.V., Nogin V.D., Pareto-optimalnye resheniya mnogokriterialnykh zadach, FIZMATLIT, Moskva, 2007
[49] Bukhtoyarov S. E., Emelichev V. A., “Mera ustoichivosti lineinoi traektornoi zadachi s sovokupno-ekstremalnym printsipom optimalnosti”, Vestn. Belorus. gos. un-ta. Ser. 1, 2002, no. 3, 84–87 | MR
[50] Sotskov Yu.N., Leontev V.K., Gordeev E.N., “Some concepts of stability analysis in combinatorial optimization”, Discrete Appl. Math., 58:2 (1995), 169–190 | DOI | MR | Zbl
[51] Emelichev V.A., Mychkov V.I., “Postoptimalnyi analiz vektornogo varianta odnoi investitsionnoi zadachi”, Trudy In-ta matem. NAN Belarusi, 2016, no. 1, 9–18 | MR | Zbl