Second-Order Optimality Conditions for Nonconvex Set-Constrained Optimization Problems

Published Online:https://doi.org/10.1287/moor.2021.1211

References

  • [1] Bai K, Ye JJ, Zhang J (2019) Directional quasi-/pseudo-normality as sufficient conditions for metric subregularity. SIAM J. Optim. 29(4):2625–2649.CrossrefGoogle Scholar
  • [2] Benko M, Gfrerer H, Outrata JV (2019) Calculus for directional limiting normal cones and subdifferentials. Set-Valued Variational Anal. 27(3):713–745.CrossrefGoogle Scholar
  • [3] Benko M, Gfrerer H, Ye JJ, Zhang J, Zhou JC (2021) Second-order optimality conditions for a class of general optimization problems. Forthcoming.Google Scholar
  • [4] Bonnans JF, Ramírez H (2005) Perturbation analysis of second-order cone programming problems. Math. Programming 104(2):205–227.CrossrefGoogle Scholar
  • [5] Bonnans JF, Shapiro A (2000) Perturbation Analysis of Optimization Problems (Springer, New York).CrossrefGoogle Scholar
  • [6] Bonnans JF, Cominetti R, Shapiro A (1999) Second order optimality conditions based on parabolic second order tangent sets. SIAM J. Optim. 9(2):466–492.CrossrefGoogle Scholar
  • [7] Chen JS, Ye JJ, Zhang J, Zhou JC (2019) Exact formula for the second-order tangent set of the second-order cone complementarity set. SIAM J. Optim. 29(4):2986–3011.CrossrefGoogle Scholar
  • [8] Clarke FH (1983) Optimization and Nonsmooth Analysis (Wiley-Interscience, New York).Google Scholar
  • [9] Ding C, Sun DF, Ye JJ (2014) First order optimality conditions for mathematical programs with semidefinite cone complementarity constraints. Math. Programming 147(1):539–579.CrossrefGoogle Scholar
  • [10] Dontchev AL, Rockafellar RT (2014) Implicit Functions and Solution Mappings (Springer, New York).Google Scholar
  • [11] Flegel ML, Kanzow C, Outrata JV (2007) Optimality conditions for disjunctive programs with application to mathematical programs with equilibrium constraints. Set-Valued Anal. 15(2):139–162.CrossrefGoogle Scholar
  • [12] Gfrerer H (2011) First order and second order characterizations of metric subregularity and calmness of constraint set mappings. SIAM J. Optim. 21(4):1439–1474.CrossrefGoogle Scholar
  • [13] Gfrerer H (2013) On directional metric regularity, subregularity and optimality conditions for nonsmooth mathematical programs. Set-Valued Variational Anal. 21(2):151–176.CrossrefGoogle Scholar
  • [14] Gfrerer H (2014) Optimality conditions for disjunctive programs based on generalized differentiation with application to mathematical programs with equilibrium constraints. SIAM J. Optim. 24(2):898–931.CrossrefGoogle Scholar
  • [15] Gfrerer H (2019) Linearized M-stationarity conditions for general optimization problems. Set-Valued Variational Anal. 27(3):819–840.CrossrefGoogle Scholar
  • [16] Gfrerer H, Klatte D (2016) Lipschitz and Hölder stability of optimization problems and generalized equations. Math. Programming 158(1):35–75.CrossrefGoogle Scholar
  • [17] Gfrerer H, Outrata JV (2016a) On computation of generalized derivatives of the normal-cone mapping and their applications. Math. Oper. Res. 41(4):1535–1556.LinkGoogle Scholar
  • [18] Gfrerer H, Outrata JV (2016b) On Lipschitzian properties of implicit multifunctions. SIAM J. Optim. 26(4):2160–2189.CrossrefGoogle Scholar
  • [19] Gfrerer H, Ye JJ (2017) New constraint qualifications for mathematical programs with equilibrium constraints via variational analysis. SIAM J. Optim. 27(2):842–865.CrossrefGoogle Scholar
  • [20] Ginchev I, Mordukhovich BS (2011) On directionally dependent subdifferentials. Comptes rendus de l’Académie bulgare des Sciences 24:497–508.Google Scholar
  • [21] Guo L, Lin GH, Ye JJ (2013) Second-order optimality conditions for mathematical programs with equilibrium constraints. J. Optim. Theory Appl. 158(1):33–64.CrossrefGoogle Scholar
  • [22] Henrion R, Outrata JV (2005) Calmness of constraint systems with applications. Math. Programming 104(2):437–464.CrossrefGoogle Scholar
  • [23] Luo ZQ, Pang JS, Ralph D (1996) Mathematical Programs with Equilibrium Constraints (Cambridge University Press, Cambridge).CrossrefGoogle Scholar
  • [24] Mehlitz P (2020) On the linear independence constraint qualification in disjunctive programming. Optim. 69(10):2241–2277.CrossrefGoogle Scholar
  • [25] Mohammadi A, Mordukhovich BS, Sarabi ME (2021) Parabolic regularity in geometric variational analysis. Trans. Amer. Math. Soc. 374(3):1711–1763.CrossrefGoogle Scholar
  • [26] Mordukhovich BS (2006) Variational Analysis and Generalized Differentiation, I: Basic Theory, II: Applications (Springer, Berlin).CrossrefGoogle Scholar
  • [27] Penot JP (1994) Optimality conditions in mathematical programming and composite optimization. Math. Programming 67(1):225–245.CrossrefGoogle Scholar
  • [28] Penot JP (1998) Second-order conditions for optimization problems with constraints. SIAM J. Control Optim. 37(1):303–318.CrossrefGoogle Scholar
  • [29] Robinson SM (1981) Some continuity properties of polyhedral multifunctions. Math. Programming Stud. 14:206–214.CrossrefGoogle Scholar
  • [30] Rockafellar RT (1970) Convex Analysis (Princeton University Press, Princeton).CrossrefGoogle Scholar
  • [31] Rockafellar RT, Wets RJB (1998) Variational Analysis (Springer, Berlin).CrossrefGoogle Scholar
  • [32] Scheel H, Scholtes S (2000) Mathematical programs with complementarity constraints: stationarity, optimality, and sensitivity. Math. Oper. Res. 25(1):1–22.LinkGoogle Scholar
  • [33] Ye JJ, Ye XY (1997) Necessary optimality conditions for optimization problems with variational inequality constraints. Math. Oper. Res. 22(4):977–997.LinkGoogle Scholar
  • [34] Ye JJ, Zhou JC (2016) First-order optimality conditions for mathematical programs with second-order cone complementarity constraints. SIAM J. Optim. 26(4):2820–2846.CrossrefGoogle Scholar
  • [35] Ye JJ, Zhou JC (2018) Verifiable sufficient conditions for the error bound property of second-order cone complementarity problems. Math. Programming 171(1):361–395.CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.