# Global linear and quadratic one-step smoothing newton method for vertical linear complementarity problems

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## Abstract

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 words

vertical linear complementarity problems smoothing Newton method global linear convergence quadratic convergence## Chinese Library Classification

O177.91## 2000 MR Subject Classification

65K10 90C33 90C30## Preview

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