A new equivalent single-level problem for bilevel problems

References

• Amahroq , T and Taa , A . 1997 . On Lagrange-Kuhn-Tucker multipliers for multiobjective optimization problems . Optimization , 41 : 159 – 172 .
   Google Scholar
• Babahadda , H and Gadhi , N . 2006 . Necessary optimality conditions for Bilevel optimization problems using convexificators . J. Global Optim. , 34 : 535 – 549 .
   Web of Science ®Google Scholar
• Bard , JF . 1991 . Some properties of the bilevel programming problem . J. Optim. Theory Appl. , 68 : 371 – 378 .
   Web of Science ®Google Scholar
• Clarke , FH . 1983 . Optimization and Nonsmooth Analysis , New York : Wiley-Interscience .
   Google Scholar
• Combari , C , Laghdir , M and Thibault , L . 1994 . Sous-différentiel de fonctions convexes composées . Ann. Sci. Math. Québec , 18 : 119 – 148 .
   Google Scholar
• Dempe , S . 1992 . A Necessary and a sufficient optimality condition for bilevel programming problem . Optimization , 25 : 341 – 354 .
   Google Scholar
• Dempe , S . 1997 . First-order necessary optimality conditions for general bilevel programming problems . J. Optim. Theory Appl. , 95 : 735 – 739 .
   Web of Science ®Google Scholar
• Dempe , S and Dutta , J . 2012 . Is bilevel programming a special case of a mathematical program with complementarity constraints? . Math. Program. , 131 : 37 – 48 .
   Web of Science ®Google Scholar
• Dempe , S and Gadhi , N . 2007 . Necessary optimality conditions for bilevel set optimization problems . J. Global Optim. , 39 : 529 – 542 .
   Web of Science ®Google Scholar
• Göpfert , A , Riahi , H , Tammer , C and Zàlinescu , C . 2003 . “ Variational Methods in Partially Ordered Spaces ” . In Canadian Mathematical Society , New York : Springer-Verlag .
   Google Scholar
• Jourani , A . 1993 . Formules d'Intersection dans un Espace de Banach . C. R. Acad. Sci. Paris , 317 : 825 – 828 .
   Google Scholar
• Outrata , JV . 1993 . On necessary optimality conditions for stackelberg problems . J. Optim. Theory Appl. , 76 : 306 – 320 .
   Web of Science ®Google Scholar
• Rockafellar , RT . 1980 . Generalized directional derivatives and subgradients of non-convex functions . Can. J. Math. , 32 : 175 – 180 .
   Web of Science ®Google Scholar
• Ye , JJ and Zhu , DL . 1995 . Optimality conditions for bilevel programming problems . Optimization , 33 : 9 – 27 .
   Google Scholar
• Zhang , R . 1993 . Problems of hierarchical optimization in finite dimensions . SIAM J. Optim. , 4 : 521 – 536 .
   Web of Science ®Google Scholar