Geodesic
Weak Convexity of Functions and the Infimal Convolution
Journal of convex analysis, Tome 23 (2016) no. 3, pp. 719-732
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In terms of sup-inf convolutions we characterize the class CWC(γ) of convolutionally weakly convex functions, that is a special class of Φ-convex functions, generated by the function γ . Motivated by Moreau-Yosida and Lasry-Lions regularizations, we consider a subclass of CWC(γ), namely, the class RCWC(γ) of regularly convolutionally weakly convex functions. We show that under reasonable assumptions on γ the class RCWC(γ) is the same as the class WC(γ), introduced from other considerations.
Classification : 41A50, 41A65, 52A21
Mots-clés : Weak convexity, infimal convolution, Moreau-Yosida regularization, Lasry-Lions regularizations 
@article{JCA_2016_23_3_JCA_2016_23_3_a4,
     author = {G. E. Ivanov},
     title = {Weak {Convexity} of {Functions} and the {Infimal} {Convolution}},
     journal = {Journal of convex analysis},
     pages = {719--732},
     year = {2016},
     volume = {23},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2016_23_3_JCA_2016_23_3_a4/}
}
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G. E. Ivanov. Weak Convexity of Functions and the Infimal Convolution. Journal of convex analysis, Tome 23 (2016) no. 3, pp. 719-732. http://geodesic.mathdoc.fr/item/JCA_2016_23_3_JCA_2016_23_3_a4/