ISSN:
1573-2916
Keywords:
Clarke subdifferential
;
Michel–Penot subdifferential
;
quasidifferential
;
convexificator
;
mean-value theorem
;
nonsmooth analysis.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Certain useful basic results of the gradient (in the smooth case), the Clarkesubdifferential, the Michel–Penot subdifferential, which is also known asthe "small" subdifferential, and the directional derivative(in the nonsmooth case) are stated and discussed. One of the advantages ofthe Michel–Penot subdifferential is the fact that it is in general "smaller"than the Clarke subdifferential. In this paper it is shown that there existsubdifferentials which may be smaller than the Michel–Penot subdifferentialandwhich have certain useful calculus. It isfurther shown that in the case of quasidifferentiability, the Michel–Penotsubdifferential enjoys calculus whichhold for the Clarke subdifferential only in the regular case.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1008246130864
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