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 subdifferential, directionally regular function, approximate convex function, subdifferentially and directionally stable function

MSC Classifications:

49J52, 46N10, 58C20 show english descriptions Nonsmooth analysis [See also 46G05, 58C50, 90C56]
Applications in optimization, convex analysis, mathematical programming, economics
Differentiation theory (Gateaux, Frechet, etc.) [See also 26Exx, 46G05] 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]

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