Smoothing Functions for Second-Order-Cone Complementarity Problems

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