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Regularizing with Bregman-Moreau envelopes. (arXiv:1705.06019v1 [math.FA])
来源于:arXiv
Moreau's seminal paper, introducing what is now called the Moreau envelope
and the proximity operator (a.k.a. proximal mapping), appeared in 1965. The
Moreau envelope of a given convex function provides a regularized version which
has additional desirable properties such as differentiability and full domain.
Fifty years ago, Attouch proposed to use the Moreau envelope for
regularization. Since then, this branch of convex analysis has developed in
many fruitful directions. In 1967, Bregman introduced what is nowadays the
Bregman distance as a measure of discrepancy between two points generalizing
the square of the Euclidean distance. Proximity operators based on the Bregman
distance have become a topic of significant research as they are useful in
algorithmic solution of optimization problems. More recently, in 2012, Kan and
Song studied regularization aspects of the left Bregman-Moreau envelope even
for nonconvex functions.
In this paper, we complement previous works by analyzing the l 查看全文>>