The test problem generation for quadratic-linear pessimistic bilevel optimization
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 17 (2014) no. 3, pp. 245-257.

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The generation method of quadratic-linear bilevel optimization test problems in a pessimistic formulation is proposed and justified. The propositions about the exact form and the number of local and global pessimistic solutions in generated problems are proved.
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A. V. Orlov; A. V. Malyshev. The test problem generation for quadratic-linear pessimistic bilevel optimization. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 17 (2014) no. 3, pp. 245-257. http://geodesic.mathdoc.fr/item/SJVM_2014_17_3_a2/

[1] Polyak B. T., Vvedenie v optimizatsiyu, Nauka, M., 1983 | MR

[2] Strekalovskii A. S., Orlov A. V., Bimatrichnye igry i bilineinoe programmirovanie, Fizmatlit, M., 2007 | Zbl

[3] DIMACS Implementation Challenges, URL: http://dimacs.rutgers.edu/Challenges/

[4] Hock W., Schittkowski K., Test Examples for Nonlinear Programming Codes, Lect. Notes in Economics and Math. Systems, 187, Springer-Verlag, Berlin etc., 1981 | DOI | MR | Zbl

[5] Schittkowski K., More Test Examples for Nonlinear Programming Codes, Lect. Notes in Economics and Math. Systems, 282, Springer-Verlag, Berlin etc., 1987 | DOI | MR | Zbl

[6] Floudas C. A., Pardalos P. M., A Collection of Test Problems for Constrained Global Optimization Algorithms, Lect. Notes in Economics and Math. Systems, 455, Springer-Verlag, Berlin etc., 1990 | MR | Zbl

[7] Sven Leyffer's Test Problems, URL: http://wiki.mcs.anl.gov/leyffer/index.php/Sven_Leyffers_Test_Problems'>http://wiki.mcs.anl.gov/leyffer/index.php/Sven_Leyffer's_Test_Problems

[8] Moshirvaziri K., “Construction of test problem for a class of reverse convex program”, J. of Optimization Theory and Applications, 81:2 (1994), 343–354 | DOI | MR | Zbl

[9] Moshirvaziri K., “Generalization of the construction of test problems for nonconvex optimization”, J. of Global Optimization, 5:1 (1994), 21–34 | DOI | MR | Zbl

[10] Moshirvaziri K., Amouzegar M. A., Jacobsen S. E., “Test problem construction for linear bilevel programming problem”, J. of Global Optimization, 8:3 (1996), 235–243 | DOI | MR | Zbl

[11] Moshirvaziri K., “Construction of test problems for concave minimization under linear and nonlinear constraints”, J. of Optimization Theory and Applications, 98:1 (1998), 83–108 | DOI | MR | Zbl

[12] Vicente L., Calamai P., Judice J., “Generation of disjointly constrained bilinear programing test problems”, Computational Optimization and applications, 1:3 (1992), 299–306 | DOI | MR | Zbl

[13] Calamai P., Vicente L., “Generating linear and linear-quadratic bilevel programming problems”, SIAM J. on Scientific Computing, 14:4 (1993), 770–782, (Archive) | DOI | MR | Zbl

[14] Calamai P., Vicente L., “Generating quadratic bilevel programming test problems”, ACM Transactions on Mathematical Software, 20 (1994), 103–119 | DOI | MR | Zbl

[15] Vicente L., Calamai P., Judice J., “A new technique for generating quadratic test problems”, Mathematical programming, 61 (1993), 215–231 | DOI | MR | Zbl

[16] Gaviano M., Kvasov D. E., Lera D., Sergeyev Y. D., “Algorithm 829: Software for generation of classes of test functions with known local and global minima for global optimization”, ACM Transactions on Mathematical Software, 29:4 (2003), 469–480 | DOI | MR | Zbl

[17] Dempe S., Foundations of Bilevel Programming, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2002 | MR | Zbl

[18] Germeier Yu. B., Igry s neprotivopolozhnymi interesami, Nauka, M., 1976 | MR

[19] Malyshev A. V., Strekalovskii A. S., “O vzaimosvyazi nekotorykh zadach dvukhurovnevoi i nelineinoi optimizatsii”, Izvestiya vuzov. Matematika, 2011, no. 4, 99–103 | MR | Zbl

[20] Malyshev A. V., Strekalovskii A. S., “Globalnyi poisk garantirovannykh reshenii v kvadratichno-lineinykh zadachakh dvukhurovnevoi optimizatsii”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Matematika, 4:1 (2011), 73–82 | Zbl

[21] Wiesemann W., Tsoukalas A., Kleniati P.-M., Rustem B., “Pessimistic bilevel optimization”, SIAM J. on Optimization, 23:1 (2013), 353–380 | DOI | MR | Zbl

[22] Vasilev F. P., Ivanitskii A. Yu., Lineinoe programmirovanie, Faktorial, M., 1998 | MR

[23] Bazara M., Shetti K., Nelineinoe programmirovanie. Teoriya i algoritmy, Mir, M., 1982 | MR | Zbl

[24] Ivanov B. N., Diskretnaya matematika. Algoritmy i programmy, Ucheb. posobie, Laboratoriya Bazovykh Znanii, M., 2002

[25] Kalitkin N. N., Chislennye metody, Gl. red. fiz.–mat. lit. izd-va “Nauka”, M., 1978 | MR