A barrier-based smoothing proximal point algorithm for NCPs over closed convex cones (Q2848172)

The paper deals with the proximal point algorithm to solve nonlinear complementarity problems over closed convex cones. A new barrier-based method of constructing smoothing approximations of Euclidean projectors over closed convex cones is proposed. These smoothing approximations are used in a smoothing proximal point algorithm to solve monotone nonlinear complementarity problems (NCPs) over a convex cone via the normal map equation. The convergence of the algorithm is proved under the assumption that \(F\) is monotone and a sufficient condition on the barrier is used in the construction of the smoothing approximation. The authors also demonstrate that the class of Chen-Mangasarian smoothing approximations fits into the framework of barrier-based smoothing approximations and report the results of preliminary numerical comparisons between an implementation of the proposed algorithm and the Newton-CG augmented Lagrangian method proposed by \textit{X.-Y. Zhao} et al. [ibid. 20, No. 4, 1737--1765 (2010; Zbl 1213.90175)], by applying them to several classes of semi-definite programming problems (SDPs).