On computation of limiting coderivatives of the normal-cone mapping to inequality systems and their applications

References

• Dontchev AL, Rockafellar RT. Characterization of strong regularity for variational inequalities over polyhedral convex sets. SIAM J. Optim. 1996;6:1087–1105.
   Web of Science ®Google Scholar
• Outrata JV. Optimality conditions for a class of mathematical programs with equilibrium constraints. Math. Oper. Res. 1999;24:627–644.
   Web of Science ®Google Scholar
• Henrion R, Römisch W. On M-stationarity points for a stochastic equilibrium problem under equilibrium constraints in electricity spot market modeling. Appl. Math. 2007;52:473–494.
   Web of Science ®Google Scholar
• Bonnans JF, Shapiro A. Perturbation analysis of optimization problems. New York (NY): Springer; 2000.
   Google Scholar
• Mordukhovich BS, Outrata JV. On second-order subdifferentials and their applications. SIAM J. Optim. 2001;12:139–169.
   Web of Science ®Google Scholar
• Outrata JV, Ramirez-Cabrera H. On the Aubin property of perturbed second-order cone programs. SIAM J. Optim. 2011;21:798–823.
   Web of Science ®Google Scholar
• Levy AB, Mordukhovich BS. Coderivatives in parametric optimization. Math. Prog. 2004;99:311–327.
   Web of Science ®Google Scholar
• Mordukhovich BS, Outrata JV. Coderivative analysis of quasi-variational inequalities with applications to stability and optimization. SIAM J. Optim. 2007;18:389–412.
   Web of Science ®Google Scholar
• Henrion R, Outrata JV, Surowiec T. On the coderivative of normal cone mapping to inequality systems. Nonlinear Anal. 2009;71:1213–1226.
   Web of Science ®Google Scholar
• Minchenko L, Stakhovski S. Parametric nonlinear programming problems under the relaxed constant rank condition. SIAM J. Optim. 2011;21:314–332.
   Web of Science ®Google Scholar
• Mordukhovich BS, Rockafellar RT. Second-order subdifferential calculus with applications to tilt stability in optimization. SIAM J. Optim. 2012;22:953–986.
   Web of Science ®Google Scholar
• Mordukhovich BS. Variational analysis and generalized differentiation, I: basic theory. Berlin: Springer; 2006.
   Google Scholar
• Rockafellar RT, Wets RJ-B. Variational analysis. Berlin: Springer; 1998.
   Google Scholar
• Gfrerer H. On directional metric regularity, subregularity and optimality conditions for nonsmooth mathematical programs. Set-Valued Var. Anal. 2013;21:151–176.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• Gfrerer H. On metric pseudo-(sub)regularity of multifunctions and optimality conditions for degenerated mathematical programs. Set-Valued Var. Anal. 2014;22:79–115.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• Gfrerer H, Outrata JV. On computation of generalized derivatives of the normal-cone mapping and their applications, preprint 2014, submitted.
   Google Scholar
• Avakov ER. Extremum conditions for smooth problems with equality-type constraints. USSR Comput. Math. Math. Phys. 1985;25:24–32.
   Web of Science ®Google Scholar
• Ginchev I, Mordukhovich BS. On directionally dependent subdifferentials. C. R. Bulg. Acad. Sci. 2011;64:497–508.
   Web of Science ®Google Scholar
• Gfrerer H. First order and second order characterizations of metric subregularity and calmness of constraint set mappings. SIAM J. Optim. 2011;21:1439–1474.
   Web of Science ®Google Scholar
• Bank B, Guddat J, Klatte D, Kummer B, Tammer K. Non-linear parametric optimization. Berlin: Akademie-Verlag; 1982.
   Google Scholar
• Aubin JP. Lipschitz behavior of solutions to convex minimization problems. Math. Oper. Res. 1984;9:87–111.
   Web of Science ®Google Scholar
• Dontchev AL, Rockafellar RT. Implicit functions and solution mappings. Heidelberg: Springer; 2009.
   Google Scholar
• Robinson SM. Strongly regular generalized equations. Math. Oper. Res. 1980;5:43–62.
   Web of Science ®Google Scholar
• Klatte D, Kummer B. Nonsmooth equations in optimization Regularity, calculus, methods and applications. Vol. 60, Nonconvex optimization and its applications. Dordrecht: Kluwer Academic; 2002.
   Google Scholar