Geodesic
$C^2(D)$-integral approximation of nonsmooth functions conserving $\varepsilon(D)$-extremum points
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 5, pp. 159-169

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A new nonlocal approximation method of nonsmooth or not enough smooth functions is considered in the paper. As the result we get twice differentiable functions, conserving to $\varepsilon(D)$-extremum points. Using such functions, a method of second order, converging to $\varepsilon(D)$-stationary points, is constructed. An optimization algorithm, converging to a stationary point with superlinear velocity, is described.
Keywords: Lipschitz functions, generalized gradients, Clarke subdifferentials, matrices of second derivatives, Newton's methods for Lipschitz functions. 
@article{TIMM_2010_16_5_a18,
     author = {I. M. Prudnikov},
     title = {$C^2(D)$-integral approximation of nonsmooth functions conserving $\varepsilon(D)$-extremum points},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {159--169},
     publisher = {mathdoc},
     volume = {16},
     number = {5},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2010_16_5_a18/}
}
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I. M. Prudnikov. $C^2(D)$-integral approximation of nonsmooth functions conserving $\varepsilon(D)$-extremum points. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 5, pp. 159-169. http://geodesic.mathdoc.fr/item/TIMM_2010_16_5_a18/