Uniform Approximation Of Min₂（f₁,f₂,...,f_n） By Multivariate Splines

Nonsmooth optimization has been attracting attention for many years. It concerns semi-Smooth optimization, nonsmooth complementarity and matrix cone programming, etc. A typ-ical nonsmooth function is min2(f1,f2,...,fn), which can be used in robust statistics. Typ-ical methods for nonsmooth optimization include semi-smooth methods, interior point metho-ds and smoothing methods. In this paper we present a smoothing method to smooth function min2(f1,f2,...,fn). We use splines to construct a tight and uniform approximation to min2(f1,f2,…,fn).