Two-level value function approach to non-smooth optimistic and pessimistic bilevel programs

References

• von Stackelberg HF. Marktform und Gleichgewicht. Berlin: Springer; 1934.
   Google Scholar
• Dempe S. Foundations of bilevel programming. Dordrecht: Kluwer Academic Publishers; 2002.
   Google Scholar
• Dempe S, Mordukhovich BS, Zemkoho AB. Sensitivity analysis for two-level value functions with applications to bilevel programming. SIAM J Optim. 2012;22:1309–1343. doi: 10.1137/110845197
   Web of Science ®Google Scholar
• Červinka M, Matonoha C, Outrata JV. On the computation of relaxed pessimistic solutions to MPECs. Optim Methods Softw. 2013;28:186–206. doi: 10.1080/10556788.2011.627585
   Web of Science ®Google Scholar
• Wiesemann W, Tsoukalas A, Kleniati P, et al. Pessimistic bilevel optimization. SIAM J Optim. 2013;23:353–380. doi: 10.1137/120864015
   Web of Science ®Google Scholar
• Dempe S, Mordukhovich BS, Zemkoho AB. Necessary optimality conditions in pessimistic bilevel programming. Optimization. 2014;63:505–533. doi: 10.1080/02331934.2012.696641
   Web of Science ®Google Scholar
• Outrata JV. On the numerical solution of a class of Stackelberg problems. ZOR-Math Methods Oper Res. 1990;34:255–277. doi: 10.1007/BF01416737
   Google Scholar
• Dempe S, Dutta J, Mordukhovich BS. New necessary optimality conditions in optimistic bilevel programming. Optimization. 2007;56:577–604. doi: 10.1080/02331930701617551
   Web of Science ®Google Scholar
• Mordukhovich BS. Basics of variational analysis and applications. New York: Springer; 2018.
   Google Scholar
• Mordukhovich BS, Nam NM, Phan HM. Variational analysis of marginal functions with applications to bilevel programming. J Optim Theory Appl. 2012;152:557–586. doi: 10.1007/s10957-011-9940-1
   Web of Science ®Google Scholar
• Ye JJ, Zhu DL. Optimality conditions for bilevel programming problems. Optimization. 1995;33:9–27; Erratum in Optimization 39 (1997), 361–366. doi: 10.1080/02331939508844060
   Google Scholar
• Dempe S, Zemkoho AB. On the Karush–Kuhn–Tucker reformulation of the bilevel optimization problem. Nonlinear Anal. 2014;75:1202–1218. doi: 10.1016/j.na.2011.05.097
   Web of Science ®Google Scholar
• Mordukhovich BS. Variational analysis and generalized differentiation. I: Basic theory. II: Applications. Berlin: Springer; 2006.
   Google Scholar
• Rockafellar RT, Wets RJ-B. Variational analysis. Berlin: Springer; 1998.
   Google Scholar
• Mordukhovich BS. Complete characterization of openness, metric regularity, and Lipschitzian properties of multifunctions. Trans Amer Math Soc. 1993;340:1–35. doi: 10.1090/S0002-9947-1993-1156300-4
   Web of Science ®Google Scholar
• Robinson SM. Some continuity properties of polyhedral multifunctions. Math Program Study. 1981;14:206–214. doi: 10.1007/BFb0120929
   Web of Science ®Google Scholar
• Henrion R, Jourani A, Outrata JV. On the calmness of a class of multifunctions. SIAM J Optim. 2002;13:603–618. doi: 10.1137/S1052623401395553
   Web of Science ®Google Scholar
• Henrion R, Outrata JV. A subdifferential condition for calmness of multifunctions. J Math Anal Appl. 2001;258:110–130. doi: 10.1006/jmaa.2000.7363
   Web of Science ®Google Scholar
• Mordukhovich BS, Outrata JV. Coderivative analysis of quasi-variational inclusions with applications to stability and optimization. SIAM J Optim. 2007;18:389–412. doi: 10.1137/060665609
   Web of Science ®Google Scholar
• Dempe S, Zemkoho AB. The generalized Mangasarian–Fromowitz constraint qualification and optimality conditions for bilevel programs. J Optim Theory Appl. 2011;148:46–68. doi: 10.1007/s10957-010-9744-8
   Web of Science ®Google Scholar
• Mordukhovich BS, Nam NM, Yen ND. Subgradients of marginal functions in parametric mathematical programming. Math Program. 2009;116:369–396. doi: 10.1007/s10107-007-0120-x
   Web of Science ®Google Scholar
• Mordukhovich BS, Nam NM. Variational stability and marginal functions via generalized differentiation. Math Oper Res. 30:1–18.
   Web of Science ®Google Scholar
• Dinh N, Mordukhovich BS, Nghia TTA. Subdifferentials of value functions and optimality conditions for DC and bilevel infinite and semi-infinite programs. Math Program. 2010;123:101–138. doi: 10.1007/s10107-009-0323-4
   Web of Science ®Google Scholar
• Zemkoho AB. A simple approach to optimality conditions in minmax programming. Optimization. 2014;63:385–401. doi: 10.1080/02331934.2011.653788
   Web of Science ®Google Scholar
• Mordukhovich BS, Nam NM, Yen ND. Fréchet subdifferential calculus and optimality conditions in nondifferentiable programming. Optimization. 2006;55:685–708. doi: 10.1080/02331930600816395
   Web of Science ®Google Scholar
• Henrion R, Surowiec T. On calmness conditions in convex bilevel programming. Appl Anal. 2011;90:951–970. doi: 10.1080/00036811.2010.495339
   Web of Science ®Google Scholar
• Zemkoho AB. Solving ill-posed bilevel programs. Set-Valued Var Anal. 2016;24:423–448. doi: 10.1007/s11228-016-0371-x
   Web of Science ®Google Scholar