The Moreau envelope function and proximal mapping in the sense of the Bregman distance |
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| Authors: | Chao KanWen Song |
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| Institution: | a Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, PR Chinab School of Mathematical and Sciences, Harbin Normal University, Harbin, 150025, PR China |
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| Abstract: | In this paper, we explore some properties of the Moreau envelope function eλf(x) of f and the associated proximal mapping Pλf(x) in the sense of the Bregman distance induced by a convex function g. Precisely, we study the continuity, differentiability, and Clarke regularity of the Moreau envelope function and the upper semicontinuity and single-valuedness of the proximal mapping as well as its relation to the convexity of λf+g, where λ is a positive parameter. |
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| Keywords: | Bregman distance Moreau envelope Proximal mapping Convexity Continuity Clarke regularity |
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