6533b85ffe1ef96bd12c271f
RESEARCH PRODUCT
Characterizations of convex approximate subdifferential calculus in Banach spaces
Abderrahim JouraniAbderrahim HantouteRafael Correasubject
[ MATH ] Mathematics [math]Mathematics::Functional AnalysisApproximate subdifferentialDual spaceConvex functionsApplied MathematicsGeneral MathematicsBanach spaceUniformly convex spaceSubderivativeApproximate variational principleCalculus rulesLocally convex topological vector spaceCalculusInterpolation spaceMSC: Primary 49J53 52A41 46N10[MATH]Mathematics [math]Reflexive spaceLp spaceMathematicsdescription
International audience; We establish subdifferential calculus rules for the sum of convex functions defined on normed spaces. This is achieved by means of a condition relying on the continuity behaviour of the inf-convolution of their corresponding conjugates, with respect to any given topology intermediate between the norm and the weak* topologies on the dual space. Such a condition turns out to also be necessary in Banach spaces. These results extend both the classical formulas by Hiriart-Urruty and Phelps and by Thibault.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-07-01 |