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Towards minimal assumptions for the infimal convolution regularization. (English) Zbl 0759.49003

Summary: We encompass the Moreau-Yosida regularization process by infimal convolution into a general framework. This sheds light on the assumptions required for obtaining the usual properties. In particular the class of lower-\(T^ 2\) mappings is shown to be a suitable class for performing the usual proximal regularization in open subsets of Hilbert spaces. The role of growth conditions is pointed out.

MSC:

49J45 Methods involving semicontinuity and convergence; relaxation
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