References
- Rockafellar RT, Wets B. Variational analysis. Berlin: Springer; 1998.
- Bonnans JF, Shapiro A. Perturbation analysis of optimization problems. New York (NY): Springer; 2000.
- Scholtes S. Nonconvex structures in nonlinear programming. Oper Res. 2004;52:368–383.
- Mordukhovich BS. Variational analysis and generalized differentiation, I: basic theory. Berlin: Springer; 2006.
- Mordukhovich BS. Variational analysis and generalized differentiation, II: applications. Berlin: Springer; 2006.
- Pang JS, Fukushima M. Complementarity constraint qualifications and simplified B-stationary conditions for mathematical programs with equilibrium constraints. Comput Optim Appl. 1999;13:111–136.
- Achtziger W, Kanzow C. Mathematical programs with vanishing constraints: optimality conditions and constraint qualifications. Math Program. 2008;114:69–99.
- Dorsch D, Shikhman V, Stein O. Mathematical programs with vanishing constraints: critical point theory. J Glob Optim. 2012;52:591–605.
- Hoheisel T, Kanzow C. Stationary conditions for mathematical programs with vanishing constraints using weak constraint qualifications. J. Math. Anal. Appl. 2008;337:292–310.
- Hoheisel T, Kanzow C. On the Abadie and Guignard constraint qualification for mathematical progams with vanishing constraints. Optimization. 2009;58:431–448.
- Hoheisel T, Kanzow C, Outrata JV. Exact penalty results for mathematical programs with vanishing constraints. Nonlinear Anal. 2010;72:2514–2526.
- Izmailov AF, Solodov MV. Mathematical programs with vanishing constraints: optimality conditions, sensitivity and a relaxation method. J Optim Theory Appl. 2009;142:501–532.
- Henrion R, Outrata JV, Surowiec T. On regular coderivatives in parametric equilibria with non-unique multipliers. Math Program Ser B. 2012;136:111–131.
- Gfrerer H, Outrata JV. On computation of generalized derivatives of the normal-cone mapping and their applications. Math Oper Res. 2016;41:1535–1556.
- Rockafellar RT. Convex analysis. Princeton (NJ): Princeton University Press; 1970.
- Henrion R, Outrata JV. Calmness of constraint systems with applications. Math Program Ser B. 2005;104:437–464.
- Gfrerer H, Klatte D. Lipschitz and Hölder stability of optimization problems and generalized equations. Math Program Ser A. 2016;158:35–75.
- Henrion R, Jourani A, Outrata JV. On the calmness of a class of multifunctions. SIAM J Optim. 2002;13:603–618.
- Robinson SM. Some continuity properties of polyhedral multifunctions. Math Program Stud. 1981;14:206–214.
- Flegel ML, Kanzow C, Outrata JV. Optimality conditions for disjunctive programs with application to mathematical programs with equilibrium constraints. Set-Valued Anal. 2007;15:139–162.
- Gfrerer H. On directional metric subregularity and second-order optimality conditions for a class of nonsmooth mathematical programs. SIAM J Optim. 2013;23:632–665.
- Flegel ML, Kanzow C. A direct proof for M-stationarity under MPEC-GCQ for mathematical programs with equilibrium constraints. In: Dempe S, Kalashnikov V, editors. Optimization with multivalued mappings: theory, applications and algorithms. New York, NY: Springer; 2006. p. 111–122.
- Ye JJ. Optimality conditions for optimization problems with complementarity constraints. SIAM J Optim. 1999;9:374–387.
- Flegel ML, Kanzow C. An Abadie-type constraint qualification for mathematical programs with equilibrium constraints. J Optim Theory Appl. 2005;124:595–614.
- Gfrerer H. Optimality conditions for disjunctive programs based on generalized differentiation with application to mathematical programs with equilibrium constraints. SIAM J Optim. 2014;24:898–931.
- Hoheisel T. Mathematical programs with vanishing constraints [PhD-thesis]. Julius-Maximilians-Universität Würzburg; 2009.
- Gfrerer H, Mordukhovich BS. Complete characterizations of tilt stability in nonlinear programming under weakest qualification conditions. SIAM J Optim. 2015;25:2081–2119.
- Henrion R, Kruger AY, Outrata JV. Some remarks on stability of generalized equations. J Optim Theory Appl. 2013;159:681–697.