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English version: Journal of Applied and Industrial Mathematics, 2019, 13:4, 612-622 |
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Volume 26, No 4, 2019, P. 16-33 UDC 519.8+518.25
Keywords: partition of the feasible region, bilevel subproblem, optimality condition. DOI: 10.33048/daio.2019.26.663 Vladimir L. Beresnev 1,2 Received June 10, 2019 References[1] T. Ding, L. Yao, and F. Li, A multi-uncertainty-set based two-stage robust optimization to Defender–Attacker–Defender model for power system protection, Reliab. Eng. Syst. Saf. 169, 179–186 (2018).[2] N. Alguacil, A. Delgadillo, and J. M. Arroyo, A trilevel programming approach for electric grid defense planning, Comput. Oper. Res. 41 (1), 282–290 (2014). [3] V. L. Beresnev, Mathematical models for planning development of technical means systems, Diskretn. Anal. Issled. Oper., Ser. 2, 4 (1), 4–29 (1997) [Russian]. [4] M. P. Scaparra and R. L. Church, A bilevel mixed-integer program for critical infrastructure protection planning, Comput. Oper. Res. 35, 1905–1923 (2008). [5] F. Liberatore, M. P. Scaparra, and M. S. Daskin, Analysis of facility protection strategies against an uncertain number of attacks: The stochastic $r$-interdiction median problem with fortification, Comput. Oper. Res. 38, 357–366 (2011). [6] S. Sadeghi, A. Seifi, and E. Azizi, Trilevel shortest path network interdiction with partial fortification, Comput. Ind. Eng. 106, 400–411 (2017). [7] H. Stackelberg, The Theory of the Market Economy (Oxford Univ. Press, Oxford, 1952). [8] S. Dempe, Foundations of Bilevel Programming (Kluwer Acad. Publ., Dordrecht, 2002). [9] M. Fischetti, I. Ljubic, and M. Sinnl, Benders decomposition without separability: A computational study for capacitated facility location problems, Eur. J. Oper. Res. 253 (3), 557–569 (2016). [10] S. Martello and P. Toth, Knapsack Problems: Algorithms and Computer Implementations (John Wiley & Sons, New York, NY, 1990). [11] H. Kellerer, U. Pferschy, and D. Pisinger, Knapsack Problems (Springer, Berlin, 2004). [12] Y. A. Kochetov and A. V. Plyasunov, Polynomially solvable class of linear bilevel programming problems, Diskretn. Anal. Issled. Oper., Ser. 2, 4 (2), 23–33 (1997) [Russian]. [13] A. V. Plyasunov, Linear bilevel programming problem with multivariant knapsack problem on the lower level, Diskretn. Anal. Issled. Oper., Ser. 2, 10 (1), 44–52 (2003) [Russian]. [14] J. T. Moore and J. F. Bard, The mixed integer linear bilevel programming problem, Oper. Res. 38 (5), 911–921 (1990). |
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