Seeger, A. Smoothing a nondifferentiable convex function: The technique of the rolling ball. (English) Zbl 0921.49008 Rev. Mat. Apl. 18, No. 1, 45-60 (1997). Let \(X\) be a locally convex topological linear space, \(f:X \to {\mathbb R} \cup \{+\infty\}\) a proper convex function and \(A\) a closed subset of \(X \times {\mathbb R}\). The author studies the properties of the \(A\)-regularization \(f_{A}:X \to \overline{{\mathbb R}}\) of \(f\) defined by \[ f_{A}(x) = \inf \left\{ \lambda + \Psi_{\text{epi}(f) + A}(x,\lambda): \lambda \in {\mathbb R} \right\} , \] where \(\Psi_{B}\) is the indicator of \(B\) and \(\text{ epi}(f)\) is the epigraph of \(f\). This notion extends the classical Moreau-Yosida regularization and the Lipschitz regularization of J.-B. Hiriart-Urruty [Math. Scand. 47, 123-134 (1980; Zbl 0436.26005)]. Reviewer: M.Degiovanni (Brescia) Cited in 4 Documents MSC: 49J52 Nonsmooth analysis 58C20 Differentiation theory (Gateaux, Fréchet, etc.) on manifolds Keywords:lower boundary function; infimal-convolution; regularizing kernel; subdifferential Citations:Zbl 0436.26005 PDFBibTeX XMLCite \textit{A. Seeger}, Rev. Mat. Apl. 18, No. 1, 45--60 (1997; Zbl 0921.49008)