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Zbl 1190.90230
Zheng, Xi Yin; Ng, Kung Fu
Metric subregularity and constraint qualifications for convex generalized equations in Banach spaces. (English)
[J] SIAM J. Optim. 18, No. 2, 437-460 (2007). ISSN 1052-6234; ISSN 1095-7189/e

Summary: Several notions of constraint qualifications are generalized from the setting of convex inequality systems to that of convex generalized equations. This is done and investigated in terms of the coderivatives and the normal cones, and thereby we provide some characterizations for convex generalized equations to have the metric subregularity. As applications, we establish formulas of the modulus of calmness and provide several characterizations of the calmness. Extending the classical concept of extreme boundary, we introduce a notion of recession cores of closed convex sets. Using this concept, we establish global metric subregularity (i.e., error bound) results for generalized equations.

MSC 2000:: *90C31 Sensitivity, etc.
90C25 Convex programming
49J52 Nonsmooth analysis (other weak concepts of optimality)
46B20 Geometry and structure of normed spaces

Keywords: metric subregularity; calmness; constraint qualification; normal cone; coderivative; recession core; generalized extreme point

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