  Smoothing methods have become part of the standard tool set for the study and
solution of nondifferentiable and constrained optimization problems as well as
a range of other variational and equilibrium problems. In this note we
synthesize and extend recent results due to Beck and Teboulle on infimal
convolution smoothing for convex functions with those of X. Chen on gradient
consistency for nonconvex functions. We use epi-convergence techniques to
define a notion of epi-smoothing that allows us to tap into the rich
variational structure of the subdifferential calculus for nonsmooth, nonconvex,
and nonfinite-valued functions. As an illustration of the versatility and range
of epi-smoothing techniques, the results are applied to the general constrained
optimization for which nonlinear programming is a special case.
