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English version: Journal of Applied and Industrial Mathematics, 2016, 10:3, 356369 

Volume 23, No 3, 2016, P. 3560 UDC 519.87+519.854
Keywords: publicprivate partnership, bilevel problem, approximation hierarchy, NPOhard problem, class $\Sigma^{P}_{2} O$, hybrid algorithm, local search. DOI: 10.17377/daio.2016.23.527 Sergey M. Lavlinskii ^{1} Received 11 April 2016 References[1] I. P. Glazyrina, S. M. Lavlinskii, and I. A. Kalgina, Public and private partnership in the mineral resources sector of Zabaikalskii krai: Problems and perspectives, Geogr. Prir. Resur., No. 4, 89–95, 2014.[2] I. A. Davydov, Tabu search for the discrete (rp)centroid problem, Diskretn. Anal. Issled. Oper., 19, No. 2, 19–40, 2012. [3] A. I. Kibzun, A. V. Naumov, and S. V. Ivanov, A bilevel optimization problem for railway transport hub planning, in Upravlenie bol’shimi sistemami (LargeScale Systems Control), Vol. 38, pp. 140–160, Inst. Probl. Upr., Moscow, 2012. [4] Yu. A. Kochetov, Computational bounds for local search in combinatorial optimization, Zh. Vychisl. Mat. Mat. Fiz., 48, No. 5, 788–807, 2008. Translated in Comput. Math. Math. Phys., 48, No. 5, 747–763, 2008. [5] S. M. Lavlinskii, Modeli indikativnogo planirovaniya sotsial’noekonomicheskogo razvitiya resursnogo regiona (Indicatorplanning models for social and economy development of a resource region), Izd. SO RAN, Novosibirsk, 2008. [6] S. M. Lavlinskii, Public and private partnership in a resource territory: Ecological problems, models, and perspectives, Probl. Progn., No. 1, 99–111, 2010. [7] S. M. Lavlinskii and I. A. Kalgina, Methods to estimate public and private partnership in the mineral and raw material sector of Zabaikalskii krai. Vestn. ZabGU, No. 9, 96–102, 2012. [8] S. M. Lavlinskii, A. A. Panin, and A. V. Plyasunov, A bilevel planning model for publicprivate partnership, Avtom. Telemekh., No. 11, 89–103, 2015. Translated in Autom. Remote Control, 76, No. 11, 1976–1987, 2015. [9] A. A. Panin, M. G. Pashchenko, and A. V. Plyasunov, Bilevel competitive facility location and pricing problems, Avtom. Telemekh., No. 4, 153–169, 2014. Translated in Autom. Remote Control, 75, No. 4, 715–727, 2014. [10] E. O. Rapoport On some problems of ground rent modeling in a mixed economy, Sib. Zh. Ind. Mat., 14, No. 2, 95–105, 2011. [11] C. Audet, G. Savard, and W. Zghal, New branchandcut algorithm for bilevel linear programming, J. Optim. Theory Appl., 134, No. 2, 353–370, 2007. [12] G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti Spaccamela, and M. Protasi, Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties, Springer, Berlin; Heidelberg, 1999. [13.] I. A. Davydov, Yu. A. Kochetov and E. Carrizosa, VNS heuristic for the (rp)centroid problem on the plane, Electron. Notes Discrete Math., 39, 5–12, 2012. [14] I. A. Davydov, Yu. A. Kochetov and A. V. Plyasunov, On the complexity of the (rp)centroid problem in the plane, TOP, 22, No. 2, 614–623, 2014. [15] S. Dempe, Foundations of Bilevel Programming, Kluwer Acad. Publ., Dordrecht, 2002. [16] S. T. DeNegre and T. K. Ralphs, A branchandcut algorithm for integer bilevel linear programs, in Operations Research and CyberInfrastructure, pp. 65–78 

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