Locating a maximally complementary solution of the monotone NCP by using non-interior-point smoothing algorithms

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

“…If x k j 0 → −∞ as k → +∞, using Property 2.1(e) immediately yields that p (x k j 0 , F ε k ,j 0 (x k )) → +∞. If x k j 0 → +∞ as k → +∞, noting that F j 0 (y k ) is bounded by the continuity of F j 0 , we have from (19) that F j 0 (x k ) does not tend to −∞, which in turn implies that {F j 0 (x k )+ε k x k j 0 } → +∞. From Property 2.1(e) where {x k j 0 } → +∞ and {F j 0 (x k )+ε k x k j 0 } → +∞,we also obtain that p (x k j 0 , F ε k ,j 0 (x k )) → +∞.…”

“…The NCP has attracted much attention due to its various applications in operations research, economics, and engineering [12,17,24]. There have been many methods proposed for solving the NCP, including merit function approaches [16,21,23,33], nonsmooth Newton methods [11,22,34], smoothing methods [5,18,27,32] and regularization methods [9,19,29,30]. All the aforementioned methods usually exploit so-called NCPfunctions defined as below.…”

“…The main purpose of this paper is to investigate how the generalized FB NCP-functions p with p ∈ (1, +∞) behave in a regularization semismooth Newton method for solving the NCP. It is well known that the regularization approach is designed to handle ill-posed problems which substitutes the solution of original problem with the solution of a sequence of well-posed problems whose solutions converging to the solution of the original problem; see [4,3,9,19,30] and references therein. In the context of complementarity problems, if we consider the so-called Tikhonov regularization, this scheme consists of solving a sequence of complementarity problems NCP(F ε ):…”

Smoothing newton algorithm for solving generalized complementarity problem

“…Lemma 3 is to investigate some properties of the iteration sequence generated by Algorithm 1, its proof can be found in Ref. [8].…”

Convergence of a smoothing algorithm for symmetric cone complementarity problems with a nonmonotone line search

“…Most assumptions given in the literature imply that the solution set of the problem concerned is nonempty and bounded [1] . Recently, the assumptions of global convergence of smoothing algorithms for solving complementarity problems were weakened to that the solution set of the problem concerned is only nonempty [2,3] . In addition, smoothing algorithms possess good numerical results.…”