TY - JOUR
T1 - Integration formulas via the Fenchel subdifferential of nonconvex functions
AU - Correa, Rafael
AU - García, Yboon
AU - Hantoute, Abderrahim
PY - 2012/2/1
Y1 - 2012/2/1
N2 - Starting from explicit expressions for the subdifferential of the conjugate function, we establish in the Banach space setting some integration results for the so-called epi-pointed functions. These results use the ε- subdifferential and the Fenchel subdifferential of an appropriate weak lower semicontinuous (lsc) envelope of the initial function. We apply these integration results to the construction of the lsc convex envelope either in terms of the ε-subdifferential of the nominal function or of the subdifferential of its weak lsc envelope.
AB - Starting from explicit expressions for the subdifferential of the conjugate function, we establish in the Banach space setting some integration results for the so-called epi-pointed functions. These results use the ε- subdifferential and the Fenchel subdifferential of an appropriate weak lower semicontinuous (lsc) envelope of the initial function. We apply these integration results to the construction of the lsc convex envelope either in terms of the ε-subdifferential of the nominal function or of the subdifferential of its weak lsc envelope.
KW - Conjugate function
KW - Epi-pointed functions
KW - Integration
KW - Lower semicontinuous convex envelope
KW - ε-subdifferential
KW - Conjugate function
KW - Epi-pointed functions
KW - Integration
KW - Lower semicontinuous convex envelope
KW - ε-subdifferential
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U2 - 10.1016/j.na.2011.05.085
DO - 10.1016/j.na.2011.05.085
M3 - Article in a journal
SN - 0362-546X
VL - 75
SP - 1188
EP - 1201
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
IS - 3
ER -