Approximation and regularization of arbitrary functions in Hilbert spaces by the Lasry-Lions method. (English) Zbl 0780.41021

Summary: The Lasry-Lions regularization method is extended to arbitrary functions. In particular, to any proper lower semicontinuous functions \(f: X\to \mathbb{R} \cup\{+\infty\}\) defined on a Hilbert space \(X\) and which is quadratically minorized (i.e. \(f(x)\geq -c(1+ \| x\|^ 2)\) for some \(c\geq 0\)), is associated a sequence of differentiable functions with Lipschitz continuous derivatives which approximate \(f\) from below. Some variants of the method are considered including the case of non quadratic kernels.


41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
65K10 Numerical optimization and variational techniques
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