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RAIRO-Oper. Res.
Volume 57, Number 3, May-June 2023
Page(s) 1009 - 1025
Published online 11 May 2023
  • H. Babahadda and N. Gadhi, Necessary optimality conditions for bilevel optimization problems using convexificators. J. Global Optimiz. 34 (2006) 535–549. [CrossRef] [Google Scholar]
  • J.F. Bard, Practical Bilevel Optimization: Algorithms and Applications. Kluwer, Dordrecht (1998). [CrossRef] [Google Scholar]
  • A.K. Bhurjee and G. Panda, Sufficient optimality conditions and duality theory for interval optimization problem. Ann. Oper. Res. 243 (2016) 335–348. [Google Scholar]
  • Y. Chalco-Cano, W.A. Lodwick and A. Rufian-Lizana, Optimality conditions of type KKT for optimization problem with interval-valued objective function via generalized derivative. Fuzzy Optim. Decis. Mak. 12 (2013) 305–322. [CrossRef] [MathSciNet] [Google Scholar]
  • F.H. Clarke, Optimization and Nonsmooth Analysis. Wiley-Interscience, New York (1983). [Google Scholar]
  • P.A. Clarke and A.W. Westerberg, Optimization for design problems having more than one objective. Comput. Chem. Eng. 7 (1983) 259–278. [CrossRef] [Google Scholar]
  • S. Dempe, Foundations of bilevel programming, in Part of the book series: Nonconvex Optimization and Its Applications, Vol. 61. Springer, New York, NY (2002). [Google Scholar]
  • S. Dempe, Foundations of Bilevel Programming. Kluwer, Dordrecht (2002). [Google Scholar]
  • S. Dempe, Annotated bibliography on bilevel programming and mathematical programs with equilibrium constraints. Optimization 52 (2003) 333–359. [CrossRef] [MathSciNet] [Google Scholar]
  • S. Dempe, Bilevel optimization: theory, algorithms, applications and a bibliography, in Bilevel Optimization. Springer Optimization and Its Applications, Vol. 161. Edited by S. Dempe and A. Zemkoho, Springer, Cham (2020). [CrossRef] [Google Scholar]
  • S. Dempe and S. Franke, Solution of bilevel optimization problems using the KKT approach. Optimization 68 (2019) 1471–1489. [CrossRef] [MathSciNet] [Google Scholar]
  • S. Dempe and A. Zemkoho, The generalized Mangasarian-Fromowitz constraint qualification and optimality conditions for bilevel programs. J. Optimiz. Theory Appl. 148 (2011) 46–68. [CrossRef] [Google Scholar]
  • S. Dempe, V. Kalashnikov, G.A. Pérez-Valdés and N. Kalashnykova, Bilevel Programming Problems: Theory, Algorithms and Application to Energy Networks. Springer, Berlin (2015). [CrossRef] [Google Scholar]
  • S. Dempe, O. Khamisov and Yu Kochetov, A special three-level optimization problem. J. Global Optimiz. 76 (2020) 519–531. [CrossRef] [Google Scholar]
  • S. Dempe, N. Gadhi and L. Lafhim, Optimality conditions for pessimistic bilevel problems using convexificator. Positivity 24 (2020) 1399–1417. [CrossRef] [MathSciNet] [Google Scholar]
  • S. Dempe, N. Gadhi, M. El idrissi and K. Hamdaoui, Necessary optimality conditions for a semivectorial bilevel problem under a partial calmness condition. Optimization 70 (2021) 1937–1957. [CrossRef] [MathSciNet] [Google Scholar]
  • J. Dutta and S. Chandra, Convexifactors, generalized convexity, and optimality conditions. J. Optimiz. Theory Appl. 113 (2002) 41–64. [CrossRef] [Google Scholar]
  • N.G. Gadhi, Comments on “A note on the paper “Optimality conditions for optimistic bilevel programming problem using convexifactors”“. J. Optimiz. Theory Appl. 189 (2021) 938–943. [CrossRef] [Google Scholar]
  • N. Gadhi and M. Ohda, On multiobjective bilevel optimization using tangential subdifferentials. J. Ind. Manag. Optim. 19 (2023) 4949–4958. [CrossRef] [MathSciNet] [Google Scholar]
  • A. Jayswal, I. Stancu-Minasian and I. Ahmad, On sufficiency and duality for a class of interval-valued programming problems. Appl. Math. Comput. 218 (2011) 4119–4127. [Google Scholar]
  • V. Jeyakumar and D.T. Luc, Nonsmooth calculus, minimality, and monotonicity of convexificators. J. Optimiz. Theory Appl. 101 (1999) 599–621. [CrossRef] [Google Scholar]
  • B. Kohli, Optimality conditions for optimistic bilevel programming problem using convexificators. J. Optimiz. Theory Appl. 152 (2012) 632–651. [CrossRef] [Google Scholar]
  • L. Lafhim, N. Gadhi, K. Hamdaoui and F. Rahou, Necessary optimality conditions for a bilevel multiobjective programming problem via a Ψ-reformulation. Optimization 67 (2018) 2179–2189. [Google Scholar]
  • P. Mehlitz, L.I. Minchenko and A.B. Zemkoho, A note on partial calmness for bilevel optimization problems with linearly structured lower level. Optimiz. Lett. 15 (2021) 1277–1291. [CrossRef] [Google Scholar]
  • B.S. Mordukhovich and Y. Shao, On nonconvex subdifferential calculus in Banach spaces. J. Convex Anal. 2 (1995) 211–227. [MathSciNet] [Google Scholar]
  • R.T. Rockafellar, Convex Analysis, Princeton, New Jersey (1970). [Google Scholar]
  • H.C. Wu, On interval-valued nonlinear programming problems. J. Math. Anal. Appl. 338 (2008) 299–316. [CrossRef] [MathSciNet] [Google Scholar]
  • J.J. Ye and D.L. Zhu, Optimality conditions for bilevel programming problems. Optimization 33 (1995) 9–27. [Google Scholar]
  • G. Zhang, J. Lu and Y. Gao, Multi-level Decision Making: Models, Methods and Applications, Vol. 82. Springer, Berlin (2015). [CrossRef] [Google Scholar]

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