## 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.

### MSC:

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

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