Some results on integration of subdifferentials

Zili Wu; Jane J. Ye

doi:10.1016/S0362-546X(98)00263-6

Some results on integration of subdifferentials

Zili Wu, Jane J. Ye

University of Victoria BC

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

The integration of ∂*-subdifferentials, a class of subdifferentials which includes the lower Dini subdifferential, the Frechlet subdifferential and the m-subdifferential are studied. It is proved that if lower semicontinuous functions f:X→R, g:X→(-∞,∞] are such that g-f is lower semicontinuous on a nonempty open convex subset U of X, and for each x in U, ∂*f(x) union ∂*(-f)(x) is nonempty and bounded, then g differs from f by a constant on U. This result serves to unify and extend several results in the literature.

Original language	English
Pages (from-to)	955-976
Number of pages	22
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	39
Issue number	8
DOIs	https://doi.org/10.1016/S0362-546X(98)00263-6
Publication status	Published - Mar 2000
Externally published	Yes

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Wu, Z., & Ye, J. J. (2000). Some results on integration of subdifferentials. Nonlinear Analysis, Theory, Methods and Applications, 39(8), 955-976. https://doi.org/10.1016/S0362-546X(98)00263-6

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AB - The integration of ∂*-subdifferentials, a class of subdifferentials which includes the lower Dini subdifferential, the Frechlet subdifferential and the m-subdifferential are studied. It is proved that if lower semicontinuous functions f:X→R, g:X→(-∞,∞] are such that g-f is lower semicontinuous on a nonempty open convex subset U of X, and for each x in U, ∂*f(x) union ∂*(-f)(x) is nonempty and bounded, then g differs from f by a constant on U. This result serves to unify and extend several results in the literature.

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Some results on integration of subdifferentials

Abstract

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