Geodesic
Thresholds of Prox-Boundedness of PLQ Functions
Journal of convex analysis, Tome 23 (2016) no. 3, pp. 691-718
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Introduced in the 1960s, the Moreau envelope has grown to become a key tool in nonsmooth analysis and optimization. Essentially an infimal convolution with a parametrized norm squared, the Moreau envelope is used in many applications and optimization algorithms. An important aspect in applying the Moreau envelope to nonconvex functions is determining if the function is prox-bounded, that is, if there exists a point x and a parameter r such that the Moreau envelope is finite. The infimum of all such r is called the threshold of prox-boundedness (prox-threshold) of the function f.
Classification : 49J52, 49J53, 49N10
Mots-clés : Moreau Envelope, piecewise linear-quadratic, PLQ, prox-threshold 
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     author = {W. L. Hare and C. Planiden},
     title = {Thresholds of {Prox-Boundedness} of {PLQ} {Functions}},
     journal = {Journal of convex analysis},
     pages = {691--718},
     year = {2016},
     volume = {23},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2016_23_3_JCA_2016_23_3_a3/}
}
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W. L. Hare; C. Planiden. Thresholds of Prox-Boundedness of PLQ Functions. Journal of convex analysis, Tome 23 (2016) no. 3, pp. 691-718. http://geodesic.mathdoc.fr/item/JCA_2016_23_3_JCA_2016_23_3_a3/