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Enlarged Inclusion of Subdifferentials

Published:2005-06-01
Printed: Jun 2005
• Lionel Thibault
• Dariusz Zagrodny
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Abstract

This paper studies the integration of inclusion of subdifferentials. Under various verifiable conditions, we obtain that if two proper lower semicontinuous functions $f$ and $g$ have the subdifferential of $f$ included in the $\gamma$-enlargement of the subdifferential of $g$, then the difference of those functions is $\gamma$-Lipschitz over their effective domain.
 Keywords: subdifferential, directionally regular function, approximate convex function, subdifferentially and directionally stable function
 MSC Classifications: 49J52 - Nonsmooth analysis [See also 46G05, 58C50, 90C56] 46N10 - Applications in optimization, convex analysis, mathematical programming, economics 58C20 - Differentiation theory (Gateaux, Frechet, etc.) [See also 26Exx, 46G05]