Estimates for coderivative of solution map in bilevel program

References

• Dempe S, Mordukhovich BS, Zemkoho AB. Necessary optimality conditions in pessimistic bilevel programming. Optim. 2014;63:505–533.
   Web of Science ®Google Scholar
• Dempe S. Foundations of bilevel programming. Dordrecht, The Netherlands: Kluwer; 2013.
   Google Scholar
• Mordukhovich BS. Variational analysis and applications. Cham, Switzerland: Springer; 2018.
   Google Scholar
• Ye JJ. Constraint qualifications and necessary optimality conditions for optimization problems with variational inequality constraints. SIAM J Optim. 2000;10:943–962.
   Web of Science ®Google Scholar
• Ye JJ. Necessary and sufficient optimality conditions for mathematical programs with equilibrium constraints. J Math Anal Appl. 2005;307:350–369.
   Web of Science ®Google Scholar
• Ye JJ, Zhu DL. New necessary optimality conditions for bilevel programs by combining the MPEC and value function approaches. SIAM J Optim. 2010;20:1885–1905.
   Web of Science ®Google Scholar
• Outrata JV. On the numerical solution of a class of Stackelberg problems. ZOR-Math Meth Oper Res. 1990;34:255–277.
   Google Scholar
• Ye JJ, Zhu DL. Optimality conditions for bilevel programming problems. Optim. 1995;33:9–27.
   Google Scholar
• Dempe S, Gadhi N, Zemkoho AB. New optimality conditions for the semivectorial bilevel optimization problem. J Optim Theor Appl. 2013;1:54.
   Google Scholar
• Gadhi N, Idrissi ME. An equivalent one level optimization problem to a semivectorial bilevel problem. Posit. 2018;22(1):261–274.
   Web of Science ®Google Scholar
• Mordukhovich BS, Dempe S, Zemkoho AB. Two-level value function approach to optimistic and pessimistic bilevel programs. Optim. 2019;68:433–455.
   Web of Science ®Google Scholar
• Mordukhovich BS, Dempe S, Zemkoho AB. Sensitivity analysis of two-level value functions with applications to bilevel programming. SIAM J Optim. 2012;22:1309–1343.
   Web of Science ®Google Scholar
• Mordukhovich BS, Nam NM, Phan HM. Variational analysis of marginal functions with applications to bilevel programming. J Optim Theor Appl. 2012;152:557–586.
   Web of Science ®Google Scholar
• Colson B, Marcotte P, Savard G. An overview of bilevel optimization. Ann Oper Res. 2007;153:235–256.
   Web of Science ®Google Scholar
• Dempe S. Annotated bibliography on bilevel programming and mathematical programs with equlibrium constraints. Optim. 2003;52(3):333–359.
   Web of Science ®Google Scholar
• Outrata JV, Kocvara M, Zowe J. Nosmooth approach to optimization problems with equilibrium constraints. Dordrecht: Kluwer Academic Publishers; 1998.
   Google Scholar
• Zemkoho AB. Solving ill-posed bilevel programs. Set-valued Var Anal. 2016;24:423–448.
   Web of Science ®Google Scholar
• Mordukhovich BS. Variational analysis and generalized differentiation I. basic theory. Berlin: Springer-Verlag; 2006.
   Google Scholar
• Borwein J, Zhu Q. Techniques of variational analysis. New York: Springer; 2005.
   Google Scholar
• Ngai HV, Michel T. Error bounds and implicit multifunction theorem in smooth Banach spaces and applications to optimization. Set-valued Var Anal. 2004;12(1/2):195–223.
   Google Scholar
• Ngai HV, Michel T. Error bounds for systems of lower semicontinuous functions in Asplund spaces. Math Program. 2009;116(1–2):397–427.
   Web of Science ®Google Scholar
• Wu Z, Ye JJ. Sufficient conditions for error bounds. SIAM J Optim. 2002;12(2):421–435.
   Web of Science ®Google Scholar
• Wu Z, Ye JJ. On error bounds for lower semicontinuous functions. Math Program. 2002;92(2):301–314.
   Web of Science ®Google Scholar
• Mordukhovich BS. Bilevel optimization and variational analysis. In: Bilevel optimization. Cham (Switzerland): Springer; 2020. p. 197–226.
   Google Scholar
• Mordukhovich BS, Nghia TTA. Nonsmooth cone-constrained optimization with applications to semi-infinite programming. Math Oper Res. 2014;39:301–324.
   Web of Science ®Google Scholar
• Mordukhovich BS, Nghia TTA. Subdifferentials of nonconvex supremum functions and their applications to semi-infinite and infinite programs with Lipschitzian data. SIAM J Optim. 2013;23:406–431.
   Web of Science ®Google Scholar
• Pérez-Aros P. Subdifferential formulae for the supremum of an arbitrary family of functions. SIAM J Optim. 2019;29(2):1714–1743.
   Web of Science ®Google Scholar
• Mao WH. Some new optimality conditions for semivector bilevel optimization program. Optim. 2021; DOI: 10.1080/02331934.2021.1873989
   Google Scholar
• Giannessi F. Theorems of the alternative and optimality conditions. J Optim Theor Appl. 1984;42:331–365.
   Web of Science ®Google Scholar
• Li SJ, Xu YD, You MX, et al. Constrained extremum problems and image space analysis part I: optimality conditions. J Optim Theor Appl. 2018;3:609.
   Google Scholar
• Li SJ, Xu YD, You MX, et al. Constrained extremum problems and image space analysis part II: duality and penalization. J Optim Theor Appl. 2018;3:637.
   Google Scholar
• Li SJ, Xu YD, You MX, et al. Constrained extremum problems and image space analysis part III: generalized systems. J Optim Theory Appl. 2018;3:660.
   Google Scholar