On the minimal distance between two surfaces
  This article revisits previous results presented in Optimization which were challenged later by Voisei and Zalinescu (V-Z) in the same journal. We aim to use the points of view of V-Z to modify the original results and highlight that the consideration of the so called Gao-Strang total complementary function is indeed quite useful for establishing necessary conditions for solving this problem. 
Daniel Morales-Silva and David Gao
math.OC