Reference : Metric subregularity of the convex subdifferential in Banach spaces
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Metric subregularity of the convex subdifferential in Banach spaces
Aragón Artacho, Francisco Javier mailto [University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > >]
Geoffroy, M. H. []
Journal of Nonlinear and Convex Analysis
[en] subdifferential ; metric regularity ; quadratic growth
[en] In [2] we characterized in terms of a quadratic growth condition various metric regularity properties of the subdifferential of a lower semicontinuous convex function acting in a Hilbert space. Motivated by some recent results in [16] where the authors extend to Banach spaces the characterization of the strong regularity, we extend as well the characterizations for the metric subregularity and the strong subregularity given in [2] to Banach spaces. We also notice that at least one implication in these characterizations remains valid for the limiting subdifferential without assuming convexity of the function in Asplund spaces. Additionally, we show some direct implications of the characterizations for the convergence of the proximal point algorithm, and we provide some characterizations of the metric subregularity and calmness properties of solution maps to parametric generalized equations
Luxembourg Centre for Systems Biomedicine (LCSB): Systems Biochemistry (Fleming Group)

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