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All issues Volume 55 / No 5 (September-October 2021) RAIRO-Oper. Res., 55 5 (2021) 2915-2939 References
Open Access
Issue
RAIRO-Oper. Res.
Volume 55, Number 5, September-October 2021
Page(s) 2915 - 2939
DOI https://doi.org/10.1051/ro/2021146
Published online 13 October 2021
  • J. Bracken and J. McGill, Mathematical programs with optimization problems in the constraints. Oper. Res. 21 (1973) 37–44. [Google Scholar]
  • B. Brunaud, I.E. Grossmann, Perspectives in multilevel decision-making in the process industry. Front. Eng. Manag. 4 (2017) 256–270. [Google Scholar]
  • V. Dua, N.A. Bozinis and E.N. Pistikopoulos, A multiparametric programming approach for mixed-integer quadratic engineering problems. Comput. Chem. Eng. 26 (2002) 715–733. [Google Scholar]
  • V. Dua and E.N. Pistikopoulos, An algorithm for the solution of multiparametric mixed integer linear programming problems. Ann. Oper. Res. 99 (2000) 123–139. [Google Scholar]
  • A.V. Fiacco, Sensitivity analysis for nonlinear programming using penalty methods. Math. Program. 10 (1976) 287–311. [Google Scholar]
  • A.V. Fiacco, G.P. McCormick, Nonlinear Programming: Sequential Unconstrained Minimization Techniques. J. Wiley and Sons Inc, New York, London, Sydney, Toronto (1968). [Google Scholar]
  • M. Guignard, Generalized Kuhn-Tucker conditions for mathematical programming problems in a Banach space. SIAM J. Cont. 7 (1969) 232–241. [Google Scholar]
  • J. Han, G. Zhang, Y. Hu, J. Lu, Solving tri-level programming problems using a particle swarm optimization algorithm. In: The 10th IEEE Conference on Industrial Electronics and Applications (2015) 569–574. [Google Scholar]
  • J. Han, G. Zhang, J. Lu, Y. Hu and S. Ma, Model and algorithm for multi-follower tri-level hierarchical decision-making, edited by C. Loo, K. Yap, K. Wong, A. Beng-Jin and K. Huang. In: Neural Information Processing. ICONIP 2014, Part III. Lecture Notes in Computer Science, Vol. 8836. Springer, Switzerland (2014) 398–406. [Google Scholar]
  • M. Hu and M. Fukushima, Multi-leader-follower games: models, methods and applications. J. Oper. Res. Soc. Jpn 58 (2015) 1–23. [Google Scholar]
  • L.A. Julien, On noncooperative oligopoly equilibrium in the multiple leader–follower game. Eur. J. Oper. Res. 256 (2017) 650–662. [Google Scholar]
  • S.M. Kassa, Three-level global resource allocation model for HIV control: A hierarchical decision system approach. Math. Biosci. Eng. 15 (2018) 255–273. [PubMed] [Google Scholar]
  • A.M. Kassa and S.M. Kassa, Approximate solution algorithm for multi-parametric non-convex programming problems with polyhedral constraints. Int. J. Optim. Control: Theor. Appl. 4 (2014) 89–98. [Google Scholar]
  • A.M. Kassa and S.M. Kassa, Deterministic solution approach for some classes of nonlinear multilevel programs with multiple follower. J. Global Optim. 68 (2017) 729–747. [Google Scholar]
  • A.A. Kulkarni, U.V. Shanbhag, An existence result for hierarchical Stackelberg v/s Stackelberg games. IEEE Trans. Automat. Contr. 60 (2015) 3379–3384. [Google Scholar]
  • S. Leyffer, T. Munson, Solving multi-leader-common-follower games. Optim. Methods Softw. 25 (2010) 601–623. [CrossRef] [Google Scholar]
  • K. Okuguchi, Expectations and stability in oligopoly models. In: Lecture Notes in Economics and Mathematical Systems, vol 138. Springer-Verlag, Berlin (1976). [CrossRef] [Google Scholar]
  • J.S. Pang and M. Fukushima, Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games. Comput. Manage. Sci. 2 (2005) 21–56. [Google Scholar]
  • J.S. Pang and M. Fukushima, Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games. Comput. Manage. Sci. 6 (2009) 373–375. [Google Scholar]
  • E. Pistikopoulos, M. Georgiadis, V. Dua, Multi-parametric programming: theory, algorithms and applications. Wiley-VCH Verlag GmbH & Co, KGaA (2007). [Google Scholar]
  • H.D. Sherali, A multiple leader Stackelberg model and analysis. Oper. Res. 32 (1984) 390–404. [Google Scholar]
  • C.L. Su, Analysis on the forward market equilibrium model. Oper. Res. Lett. 35 (2007) 74–82. [Google Scholar]
  • L. Sun, Equivalent bilevel programming form for the generalized Nash equilibrium problem. J. Math. Res. 2 (2010) 8–13. [Google Scholar]
  • Q. Wang, F. Yang, Y. Liu, Bilevel programs with multiple followers. J. Syst. Sci. Complex. 13 (2000) 265–276. [Google Scholar]
  • A.B. Zewde and S.M. Kassa, A method for solving some class of multilevel multi-leader multi-follower programming problems, edited by H.A. Le-Thi, H.M. Le, T. Pham-Dinh. In: Optimization of Complex Systems: Theory, Models, Algorithms and Applications. WCGO 2019. Advances in Intelligent Systems and Computing, Vol. 991. Springer Nature, Switzerland (2020) 589–599. [Google Scholar]
  • A.B. Zewde, S.M. Kassa, Multi-parametric approach for multilevel multi-leader-multi-follower games using equivalent reformulations. J. Math. Comput. Sci. 11 (2021) 2955–2980. [Google Scholar]

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