$C^2(D)$-integral approximation of nonsmooth functions conserving $\varepsilon(D)$-extremum points

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.