Smoothing functions have been much studied in the solution of
optimization and complementarity problems with
nonnegativity constraints.
In this paper, we extend smoothing functions to problems
where the nonnegative orthant is replaced
by the direct product of second-order cones.
These smoothing functions include the
Chen-Mangasarian class and the smoothed Fischer-Burmeister function.
We study the Lipschitzian and differential properties
of these functions and, in particular, we derive
computable formulas for these functions and their Jacobians.
These properties and formulas can then be used to
develop and analyze non-interior
continuation methods for solving the corresponding optimization and
complementarity problems.
In particular, we establish existence and uniqueness
of the Newton direction when the underlying mapping is monotone.