A smoothing Newton method for extended vertical linear complementarity problems

In this paper, we reformulate the extended vertical linear complementarity problem (EVLCP(m, q)) as a nonsmooth equation H(t, x) = 0, where H : Rn+1 - -> Rn+1, t is an element of R is a parameter variable, and x is an element of R is the original variable. H is continuously differentiable except at s uch points (t, x) with t = 0. Furthermore H is strongly semismooth. The ref ormulation of EVLCP(m; q) as a nonsmooth equation is based on the so-called aggregation (smoothing) function. As a result, a Newton-type method is pro posed which generates a sequence {w(k) = (t(k), x(k))} with all t(k) > 0. W e prove that every accumulation point of this sequence is a solution of EVL CP(M,q) under the assumption of row W-0-property. If row W-property holds a t the solution point, then the convergence rate is quadratic. Promising num erical results are also presented.