Nondifferentiable optimization via smooth approximation: General analytical approach

In this paper we present a method for nondifferentiable optimization, based on smoothed functionals which preserve such useful properties of the original function as convexity and continuous differentiability. We show that smoothed functionals are convenient for implementation on computers. We also show how some earlier results in nondifferentiable optimization based on smoothing-out of kink points can be fitted into the framework of smoothed functionals. We obtain polynomial approximations of any order from smoothed functionals with kernels given by Beta distributions. Applications of smoothed functionals to optimization of min-max and other problems are also discussed.