Geodesic
Global search for guaranteed solutions in quadratic-linear bilevel optimization problems
The Bulletin of Irkutsk State University. Series Mathematics, Tome 4 (2011) no. 1, pp. 73-82
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A quadratic-linear bilevel optimization problem with guaranteed (pessimistic) solution is considered. It is reduced to a series of optimistic bilevel optimization problems, which are further reduced to nonconvex optimization problems. Global and local search algorithms for the latter problems are developed. The results of computational solving randomly generated test problems are given and analyzed.
Keywords: Bilevel optimization, Pessimistic solution, Nonconvex optimization problems, Local search, Global search, Computational simulation. 
@article{IIGUM_2011_4_1_a6,
     author = {A. V. Malyshev and A. S. Strekalovsky},
     title = {Global search for guaranteed solutions in quadratic-linear bilevel optimization problems},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {73--82},
     year = {2011},
     volume = {4},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2011_4_1_a6/}
}
TY  - JOUR
AU  - A. V. Malyshev
AU  - A. S. Strekalovsky
TI  - Global search for guaranteed solutions in quadratic-linear bilevel optimization problems
JO  - The Bulletin of Irkutsk State University. Series Mathematics
PY  - 2011
SP  - 73
EP  - 82
VL  - 4
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/IIGUM_2011_4_1_a6/
LA  - ru
ID  - IIGUM_2011_4_1_a6
ER  - 
%0 Journal Article
%A A. V. Malyshev
%A A. S. Strekalovsky
%T Global search for guaranteed solutions in quadratic-linear bilevel optimization problems
%J The Bulletin of Irkutsk State University. Series Mathematics
%D 2011
%P 73-82
%V 4
%N 1
%U http://geodesic.mathdoc.fr/item/IIGUM_2011_4_1_a6/
%G ru
%F IIGUM_2011_4_1_a6
A. V. Malyshev; A. S. Strekalovsky. Global search for guaranteed solutions in quadratic-linear bilevel optimization problems. The Bulletin of Irkutsk State University. Series Mathematics, Tome 4 (2011) no. 1, pp. 73-82. http://geodesic.mathdoc.fr/item/IIGUM_2011_4_1_a6/

[1] F. P. Vasilev, Metody optimizatsii, Faktorial-press, M., 2002

[2] A. A. Vasin, V. V. Morozov, Teoriya igr i modeli matematicheskoi ekonomiki, MAKS Press, M., 2005

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

[4] V. A. Gorelik, A. F. Kononenko, Teoretiko-igrovye modeli prinyatiya reshenii v ekologo-ekonomicheskikh sistemakh, Radio i svyaz, M., 1982 | MR | Zbl

[5] A. V. Malyshev, A. S. Strekalovskii, “O vzaimosvyazi nekotorykh zadach dvukhurovnevoi i nelineinoi optimizatsii”, Izv. vuzov. Matematika, 2011, no. 4, 99–104 | MR

[6] D. A. Molodtsov, “O reshenii odnogo klassa neantagonisticheskikh igr”, Zhurn. vychisl. matematiki i mat. fiziki, 16:6 (1976), 1451–1456 | MR | Zbl

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

[8] A. C. Strekalovskii, “O minimizatsii raznosti dvukh vypuklykh funktsii na dopustimom mnozhestve”, Zhurn. vychisl. matematiki i mat. fiziki, 43:3 (2003), 399–409 | MR | Zbl

[9] A. S. Strekalovskii, Elementy nevypukloi optimizatsii, Nauka, Novosibirsk, 2003

[10] A. G. Sukharev, A. V. Timokhov, V. V. Fedorov, Kurs metodov optimizatsii, Nauka, M., 1986 | MR | Zbl

[11] J. F. Bard, Practical Bilevel Optimization, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1998 | MR

[12] M. S. Bazaraa, H. D. Sherali, C. M. Shetty, Nonlinear programming: theory and algorithms, 3rd ed., Wiley-Interscience, 2006 | MR | Zbl

[13] P. Calamai, L. Vicente, “Generating Quadratic Bilevel Programming Test Problems”, ACM Transactions on Mathematical Software, 20 (1994), 103–119 | DOI | MR | Zbl

[14] B. Colson, P. Marcotte, G. Savard, “An overview of bilevel optimization”, Annals of operations research, 153:1 (2007), 235–256 | DOI | MR | Zbl

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

[16] J. Nocedal, S. J. Wrigth, Numerical Optimization, 2nd ed., Springer, 2006 | MR

[17] A. S. Strekalovsky, A. V. Orlov, “A new approach to nonconvex optimization”, Numerical Methods and Programming, 8 (2007), 160–176 http://num-meth.srcc.msu.su/english/index.html

[18] A. Tsoukalas, W. Wiesemann, B. Rustem, “Global Optimization of Pessimistic Bi-Level Problems”, Workshop on Global Optimization — Methods and Applications, American Mathematical Society, 2009, 215–243 | MR | Zbl