On the piecewise-concave approximations of functions
  The piecewise-concave function may be used to approximate a wide range of other functions to arbitrary precision over a bounded set. In this short paper, this property is proven for three function classes: (a) the multivariate twice continuously differentiable function, (b) the univariate Lipschitz-continuous function, and (c) the multivariate separable Lipschitz-continuous function. 
Gene A. Bunin
math.OC