Department of Applied Mathematics & Physics, Kyoto University
Technical Report 2000-009 (November 06, 2000)
Smoothing Functions for Second-Order-Cone Complementarity Problems
by Masao Fukushima, Zhi-Quan Luo, and Paul Tseng
Smoothing functions have been much studied in the solution of
optimization and complementarity problems with
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
In particular, we establish existence and uniqueness
of the Newton direction when the underlying mapping is monotone.