ISSN:
1432-5217
Keywords:
Approximate subdifferential
;
topological properties
;
partial approximate subdifferential
;
nonsmooth optimization
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Economics
Notes:
Abstract Topological properties of the approximate Subdifferential introduced by Mordukhovich are studied. Apart from formulating a sufficient condition for connectedness, it is shown that, up to homeomorphy, each compact subset of ℝp may occur as the approximate subdifferential of some Lipschitz function. Furthermore, even an exact result is possible when considering the partial approximate Subdifferential, which was introduced as a parametric extension by Jourani and Thibault: Given any compact subset of ℝp, there is a locally Lipschitzian function realizing this set as its partial approximate Subdifferential at some predefined point.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01432653
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