Slater Condition for Tangent Derivatives

References

• [1] Aussel D, Daniilidis A, Thibault L (2005) Subsmooth sets: Functional characterizations and related concepts. Trans. Amer. Math. Soc. 357(4):1275–1301.Crossref, Google Scholar
• [2] Azé D, Corvellec J-N (2004) Characterizations of error bounds for lower semicontinuous functions on metric spaces. ESAIM Control Optim. Calculus Variations 10(3):409–425.Crossref, Google Scholar
• [3] Cabot A, Thibault L (2014) Sequential formulae for the normal cone to sublevel sets. Trans. Amer. Math. Soc. 366(12):6591–6628.Crossref, Google Scholar
• [4] Clarke FH (1983) Optimization and Nonsmooth Analysis (Wiley, New York).Google Scholar
• [5] Diestel J, Uhr JJ Jr (1977) Vector Measures (American Mathematical Society, Providence, RI).Crossref, Google Scholar
• [6] Dontchev AL, Rockafellar RT (2009) Implicit Functions and Solution Mappings (Springer, New York).Crossref, Google Scholar
• [7] Dontchev AL, Lewis AS, Rockafellar RT (2003) The radius of metric regularity. Trans. Amer. Math. Soc. 355(2):493–517.Crossref, Google Scholar
• [8] Fiacco AV, McCormick GP (1968) Nonlinear Programming: Sequential Unconstrained Minimization Techniques (John Wiley, New York).Google Scholar
• [9] Goberna A, López MA, eds. (2001) Semi-infinite Programming—Recent Advances (Kluwer, Boston).Crossref, Google Scholar
• [10] Hantoute A, Svensson A (2017) A general representation of δ-normal sets to sublevels of convex functions. Set-Valued Variational Anal. 25:651–678.Crossref, Google Scholar
• [11] Hettich R, Kortanek KO (1993) Semi-infinite programming: Theory, methods, and applications. SIAM Rev. 35(3):380–429.Crossref, Google Scholar
• [12] Hiriart-Urruty J-B, Lemarechal C (1993) Convex Analysis and Minimization Algorithms I. Fundamentals (Springer-Verlag, Berlin).Crossref, Google Scholar
• [13] Hoffman AJ (1952) On approximate solutions of systems of linear inequalities. J. Res. National Bureau Standards 49(4):263–265.Crossref, Google Scholar
• [14] Hu H (2005) Characterizations of the strong basic constraint qualification. Math. Oper. Res. 30(4):956–965.Link, Google Scholar
• [15] Ioffe AD (2016) Metric regularity–A survey part 1, theory. J. Australian Math. Soc. 101(2):188–243.Crossref, Google Scholar
• [16] Klatte D, Henrion R (1998) Regularity and stability in non-linear semi-infinite optimization. Reemtsen R, Rueckmann J-J, eds. Semi-infinite Programming (Kluwer Academic Publishers, Boston), 69–102.Crossref, Google Scholar
• [17] Lewis AS, Pang JS (1997) Error bounds for convex inequality systems. Crouzeix JP, ed. Generalized convexity, generalized monotonicity: Recent results (Luminy), Nonconvex Optim. Appl., 27 (Kluwer Acad. Publ., Dordrecht), 75–100.Google Scholar
• [18] Li W (1997) Abadie’s constraint qualification, metric regularity, and error bounds for differentiable convex inequalities. SIAM J. Optim. 7(4):966–978.Crossref, Google Scholar
• [19] Li W, Nahak C, Singer I (2000) Constraint qualifications for semi-infinite systems of convex inequalities. SIAM J. Optim. 11(1):31–52.Crossref, Google Scholar
• [20] López MA, Still G (2007) Semi-infinite programming. Eur. J. Oper. Res. 180(2):491–518.Crossref, Google Scholar
• [21] Megginson RE (1998) An Introduction to Banach Space Theory (Springer-Verlag, New York).Crossref, Google Scholar
• [22] Mordukhovich BS (2006) Variational Analysis and Generalized Differentiation I/II (Springer-Verlag, Berlin).Crossref, Google Scholar
• [23] Ng KF, Zheng XY (2001) Error bounds for lower semicontinuous functions in normed spaces. SIAM J. Optim. 12(1):1–17.Crossref, Google Scholar
• [24] Ngai HV, Théra M (2009) Error bounds for systems of lower semicontinuous functions in Asplund spaces. Math. Programming 116(1–2):397–427.Crossref, Google Scholar
• [25] Ngai HV, Kruger A, Théra M (2010) Stability of error bounds for semi-infinite convex constraint systems. SIAM J. Optim. 20(4):2080–2096.Crossref, Google Scholar
• [26] Pang JS (1997) Error bounds in mathematical programming. Math. Programming 79:299–332.Crossref, Google Scholar
• [27] Robinson SM (1975) An applicaiton of error bounds for convex programming in a linear space. SIAM J. Control 13(2):271–273.Crossref, Google Scholar
• [28] Robinson SM (1976) Regularity and stability for convex multivalued functions. Math. Oper. Res. 1(2):130–143.Link, Google Scholar
• [29] Shapiro A (2009) Semi-infinite programming, duality, discretization and optimality conditions. Optim. 58(2):133–161.Crossref, Google Scholar
• [30] Wu Z, Ye JJ (2002) On error bounds for lower semicontinuous functions. Math. Programming 92(2):301–314.Crossref, Google Scholar
• [31] Zalinescu C (2001) Weak sharp minima, well-behaving functions and global error bounds for convex inequalities in Banach spaces. Proc. 12th Baikal Internat. Conf. Optim. Methods Their Appl., 272–284.Google Scholar
• [32] Zheng XY, Ng KF (2004) Error bound moduli for conic convex systems on Banach spaces. Math. Oper. Res. 29(2):213–228.Link, Google Scholar
• [33] Zheng XY, Ng KF (2007) Metric subregularity and constraint qualifications for convex generalized equations in Banach spaces. SIAM J. Optim. 18(2):437–460.Crossref, Google Scholar
• [34] Zheng XY, Ng KF (2010) Metric subregularity and calmness for nonconvex generalized equations in Banach spaces. SIAM J. Optim. 20(5):2119–2136.Crossref, Google Scholar
• [35] Zheng XY, Ng KF (2012) Subsmooth semi-infinite and infinite optimization problems. Math. Programming 134(2):365–393.Crossref, Google Scholar
• [36] Zheng XY, Ng KF (2019) Stability of error bounds for conic subsmooth inequalities. ESAIM Control Optim. Calculus Variations 25:55.Crossref, Google Scholar
• [37] Zheng XY, Wei Z (2012) Perturbation analysis of error bounds for quasi-subsmooth inequalities and semi-infinite constraint systems. SIAM J. Optim. 22(1):41–65.Crossref, Google Scholar