A primal-dual algorithm for minimizing a sum of Euclidean norms
Journal of Computational and Applied Mathematics
Quadratic one-step smoothing Newton method for P0-LCP without strict complementarity
Applied Mathematics and Computation
Smooth Convex Approximation to the Maximum Eigenvalue Function
Journal of Global Optimization
Global error bounds for the extended vertical LCP
Computational Optimization and Applications
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In this paper, we reformulate the extended vertical linear complementarity problem (EVLCP(m,q)) as a nonsmooth equation H(t,x)=0, where $H: \mbox{\smallBbb R}^{n+1} \to \mbox{\smallBbb R}^{n+1}$, $t \in \mbox{\smallBbb R}$ is a parameter variable, and $x \in \mbox{\smallBbb R}$ is the original variable. H is continuously differentiable except at such points (t,x) with t=0. Furthermore H is strongly semismooth. The reformulation 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 proposed which generates a sequence {wk=(tk,xk)} with all tk 0. We prove that every accumulation point of this sequence is a solution of EVLCP(M, q) under the assumption of row ${\cal W}_0$-property. If row ${\cal W}$-property holds at the solution point, then the convergence rate is quadratic. Promising numerical results are also presented.