Global linear and quadratic one-step smoothing newton method for vertical linear complementarity problems
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A one-step smoothing Newton method is proposed for solving the vertical linear complementarity problem based on the so-called aggregation function. The proposed algorithm has the following good features: (i) It solves only one linear system of equations and does only one line search at each iteration; (ii) It is well-defined for the vertical linear complementarity problem with vertical block P 0 matrix and any accumulation point of iteration sequence is its solution. Moreover, the iteration sequence is bounded for the vertical linear complementarity problem with vertical block P 0 +R 0 matrix; (iii) It has both global linear and local quadratic convergence without strict complementarity. Many existing smoothing Newton methods do not have the property (iii).
Key wordsvertical linear complementarity problems smoothing Newton method global linear convergence quadratic convergence
Chinese Library ClassificationO177.91
2000 MR Subject Classification65K10 90C33 90C30
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