A regularization semismooth Newton method based on the generalized Fischer–Burmeister function for P0-NCPs

Abstract

We consider a regularization method for nonlinear complementarity problems with F being a P 0 -function which replaces the original problem with a sequence of the regularized complementarity problems. In this paper, this sequence of regularized complementarity problems are solved approximately by applying the generalized Newton method for an equivalent augmented system of equations, constructed by the generalized Fischer-Burmeister (FB) NCP-functions p with p > 1. We test the performance of the regularization semismooth Newton method based on the family of NCP-functions through solving all test problems from MCPLIB. Numerical experiments indicate that the method associated with a smaller p, for example p ∈ [1.1, 2], usually has better numerical performance, and the generalized FB functions p with p ∈ [1.1, 2) can be used as the substitutions for the FB function 2 .

The linear convergence of a derivative-free descent method for nonlinear complementarity problems

“…Various methods for solving the NCP have been proposed in the literature (see, for example, [2,3,4,5,6,10,11,12,13,14,15,16,17,18,19,20,23,24]). Among which, one of the most popular and powerful approaches is to reformulate the NCP as an unconstrained minimization problem [2,4,5,7,8,9,18,19,20,24]. This kind of methods is called the merit function method, where the merit function is generally constructed by some NCP-function.…”

“…The NCP-function φ p was introduced by Luo and Tseng [19], and further studied by Chen [2] and Chen and Pan [4,5]. Obviously, when p = 2, the NCP-function φ p reduces the Fischer-Burmeister NCP-function φ F B (a, b) = √ a 2 + b 2 − (a + b).…”