Reference : Metric subregularity of the convex subdifferential in Banach spaces
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/12003
Metric subregularity of the convex subdifferential in Banach spaces
English
Aragón Artacho, Francisco Javier mailto [University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > >]
Geoffroy, M. H. []
2014
Journal of Nonlinear and Convex Analysis
15
1
35-47
Yes
International
[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)
http://hdl.handle.net/10993/12003
http://www.ybook.co.jp/online2/jncav15.html

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