Lower semicontinuous type regularity conditions for subdifferential calculus

Abstract

We give a lower semicontinuous type regularity condition and a closedness type one which turn out to be necessary and sufficient for the fulfilment of two different formulae involving the ϵ-subdifferential of a perturbation function, respectively. These regularity conditions prove to be sufficient also for having formulae for the classical subdifferential of a perturbation function. Some recently published results concerning ϵ-subdifferentials are rediscovered as special cases.

Keywords:

• conjugate functions
• convex subdifferentials
• regularity conditions
• stable strong duality
• composed convex functions

AMS Subject Classification :

• 90C46
• 49N15
• 90C25

Acknowledgement

Research partially supported by DFG (German Research Foundation), project WA 922/1-3.