A Double Nonmonotone Quasi-Newton Method for Nonlinear Complementarity Problem Based on Piecewise NCP Functions

Algorithm 1

	Step 0: initialization.
	Given initial point , , , , , .
	Step 1: if , then stop. Otherwise, calculate the search direction
	. (a)
	By (a), we can obtain and .
	Step 2: modified linear search technique.
	Step 2.1 If
	, (b)
	, (c)
	, (d)
	where , is a positive constant. Then, let
	, (e)
	and go to Step 3; otherwise, go to Step 2.2.
	Step 2.2: for , check the following inequality with successively
	, (f)
	, (g)
	Let be the smallest nonnegative integer such that (f) and (g) hold for . Set , and
	, (h)
	and go to Step 3.
	Step 3: Update to get ,
	, (i)
	where
	. (j)
	Select to satisfy and matrix is nonsingular.
	Step 4: Let , go to Step 1.