Document Type

Technical Report


In this paper we study infimal convolutions of extended-real-valued functions in Hilbert spaces paying a special attention to a rather broad and remarkable class of prox-regular functions. Such functions have been well recognized as highly important in many aspects of variational analysis and its applications in both finite-dimensional and infinite-dimensional settings. Based on advanced variational techniques, we discover some new sub differential properties of infima! convolutions and apply them to the study of Lipschitzian behavior of subdifferentials for prox-regular functions in Hilbert spaces. It is shown, in particular, that the fulfillment of a natural Lipschitz-like property for (set-valued) sub differentials of prox-regular functions forces such functions, under weak assumptions, actually to be locally smooth with single-valued subdifferentials reduced to Lipschitz continuous gradient mappings.

Number in Series



Applied Mathematics | Mathematics

AMS Subject Classification



The paper is dedicated to Hedi Attouch on the occasion of his sixtieth birthday. This research was supported in part by the ARC Discovery grants DP0664423 and DP0987445, and also partly supported by the US National Science Foundation under grant DMS-0603846.