Strong calmness of perturbed KKT system for a class of conic programming with degenerate solutions

References

• Bonnans JF, Cominetti R, Shapiro A. Second-order optimality conditions based on parabolic second-order tangent sets. SIAM J Optim. 1999;9:466–492. doi: 10.1137/S1052623496306760
   Web of Science ®Google Scholar
• Bonnans JF, Ramírez HC. Perturbation analysis of second-order cone programming problems. Math Program. 2005;104:205–227. doi: 10.1007/s10107-005-0613-4
   Web of Science ®Google Scholar
• Ding C, Sun DF, Toh KC. An introduction to a class of matrix cone programming. Math Program. 2014;144:141–179. doi: 10.1007/s10107-012-0619-7
   Web of Science ®Google Scholar
• Rockafellar RT. Convex analysis. Princeton (NJ): Princeton University Press; 1970.
   Google Scholar
• Robinson SM. Some continuity properties of polyhedral multifunctions. Math Program Stud. 1981;14:206–214. doi: 10.1007/BFb0120929
   Web of Science ®Google Scholar
• Dontchev AL, Rockafellar RT. Implicit functions and solution mappings-a view from variational analysis. New York: Springer; 2009.
   Google Scholar
• Fernández D, Solodov M. Stabilized sequential quadratic programming for optimization and a stabilized Newton-type method for variational problems. Math Program. 2010;125:47–73. doi: 10.1007/s10107-008-0255-4
   Web of Science ®Google Scholar
• Fischer A. Local behavior of an iterative framework for generalized equations with nonisolated solutions. Math Program. 2002;94:91–124. doi: 10.1007/s10107-002-0364-4
   Web of Science ®Google Scholar
• Izmailov AF, Solodov MV. Stabilized SQP revisited. Math Program. 2012;133:93–120. doi: 10.1007/s10107-010-0413-3
   Web of Science ®Google Scholar
• Izmailov AF, Kurennoy AS, Solodov MV. A note on upper Lipschitz stability, error bounds, and critical multipliers for Lipschitz-continuous KKT systems. Math Program. 2013;142:591–604. doi: 10.1007/s10107-012-0586-z
   Web of Science ®Google Scholar
• Hager W, Gowda M. Stability in the presence of degeneracy and error estimation. Math Program. 1999;85:181–192. doi: 10.1007/s101070050051
   Web of Science ®Google Scholar
• Izmailov AF, Kurennoy AS, Solodov MV. Local convergence of the method of multipliers for variational and optimization problems under the noncriticality assumption. Comput Optim Appl. 2015;60:111–140. doi: 10.1007/s10589-014-9658-8
   Web of Science ®Google Scholar
• Wright SJ. Superlinear convergence of a stabilized SQP method to a degenerate Solution. Comput Optim Appl. 1998;11:253–275. doi: 10.1023/A:1018665102534
   Web of Science ®Google Scholar
• Cui Y, Sun DF, Toh KC. On the asymptotic superlinear convergence of the augmented Lagrangian method for semidefinite programming with multiple solutions. 2016, arXiv: 1610.00875v1.
   Google Scholar
• Zhang TY, Zhang LW. Critical multipliers in semidefinite programming. 2018, arXiv: 1801.02218v1.
   Google Scholar
• Rockafellar RT, Wets JB. Variational analysis. New York: Springer; 1998.
   Google Scholar
• Mordukhovich BS. Variational analysis and generalized differentiation I & II. Berlin Heidelberg: Springer-Verlag; 2006.
   Google Scholar
• Mordukhovich BS. Maximum principle in problems of time optimal control with nonsmooth constraints. J Appl Math Mech. 1976;40:960–969. doi: 10.1016/0021-8928(76)90136-2
   Web of Science ®Google Scholar
• Klatte D, Kummer B. Constrained minima and Lipschitizan penalties in metric spaces. SIAM J Optim. 2002;13:619–633. doi: 10.1137/S105262340139625X
   Web of Science ®Google Scholar
• Aubin JP. Contingent derivatives of set-valued maps and existence of solutions to nonlinear inclusions and differential inclusions in mathematical analysis and applications. In: Nachbin L, editors. Advances in mathematics: supplementary studies, 7A. New York: Academic Press; 1960. p. 160–232.
   Google Scholar
• King AJ, Rockafellar RT. Sensitivity analysis for nonsmooth generalized equations. Math Program. 1992;55:193–212. doi: 10.1007/BF01581199
   Web of Science ®Google Scholar
• Levy AB. Implicit multifunction theorems for the sensitivity analysis of variational conditions. Math Program. 1996;74:333–350.
   Web of Science ®Google Scholar
• Bonnans JF, Shapiro A. Perturbation analysis of optimization problems. New York: Springer; 2000.
   Google Scholar
• Bonnans JF, Cominetti R, Shapiro A. Sensitivity analysis of optimization problems under second order regular constraints. Math Oper Res. 1998;23:806–831. doi: 10.1287/moor.23.4.806
   Web of Science ®Google Scholar
• Wu J, Zhang LW, Zhang Y. Mathematical programs with semidefinite cone complementarity constraints: constraint qualifications and optimality conditions. Set-Valued Var Anal. 2014;22:155–187. doi: 10.1007/s11228-013-0242-7
   Web of Science ®Google Scholar
• Ding C, Sun DF, Zhang LW. Characterization of the robust isolated calmness for a class of conic programming problems. SIAM J Optim. 2017;27:67–90. doi: 10.1137/16M1058753
   Web of Science ®Google Scholar
• Liu YL, Pan SH. Computation of graphical derivatives of normal cone maps to a class of conic constraint sets. 2017. DOI:10.1007/s11228-018-0494-3
   Google Scholar
• Bauschke HH, Borwein JM, Li W. Strong conical hull intersection property, bounded linear regularity, Jamesons property (G), and error bounds in convex optimization. Math Program. 1999;86:135–160. doi: 10.1007/s101070050083
   Web of Science ®Google Scholar
• Ioffe AD, Outrata JV. On metric and calmness qualification conditions in subdifferential calculus. Set-Valued Anal. 2008;16:199–227. doi: 10.1007/s11228-008-0076-x
   Google Scholar
• Gfrerer H, Mordukhovich BS. Second-order variational analysis of parametric constraint and variational systems. 2017, arXiv:1711.07082v1.
   Google Scholar
• Gfrerer H, Outrara JV. On computation of generalized derivatives of the normal-cone mapping and their applications. Math Oper Res. 2016;41:1535–1556. doi: 10.1287/moor.2016.0789
   Web of Science ®Google Scholar
• Henrion R, Outrata JV. Calmness of constraint systems with applications. Math Program. 2005;104:437–464. doi: 10.1007/s10107-005-0623-2
   Web of Science ®Google Scholar
• Robinson SM. Generalized equations and their solutions, part II: applications to nonlinear programming. Math Program Stu. 1982;10:200–221. doi: 10.1007/BFb0120989
   Google Scholar