Abstract
In this paper, by extending the classical Newton method, we present the generalized Newton method (GNM) with high-order convergence for solving a class of large-scale linear complementarity problems, which is based on an additional parameter and a modulus-based nonlinear function. Theoretically, the performance of high-order convergence is analyzed in detail. Some numerical experiments further demonstrate the efficiency of the proposed new method.
Highlights
Many efficient methods were developed to solve linear complementarity problem
We consider the linear complementarity problem, abbreviated as LCP(q, A), to find a vector u ∈ Rn such that ⎧ ⎪⎨u ≥, ⎪⎩wwT:=u Au + =, q ≥ ( . )where A ∈ Rn×n and q ∈ Rn are a given real matrix and a real vector, respectively
By introducing a smooth equation and some reasonable equivalent reformulations, we investigate a generalized Newton iteration method with high-order convergence rate for solving a class of large-scale linear complementarity problem, which make full use of the superiority of the second-order convergence rate of the classical Newton method
Summary
Many efficient methods were developed to solve linear complementarity problem. In many works were considered by Bai et al to solve the linear complementarity problem in [ – ]. The modulus-based synchronous multisplitting iteration methods for large sparse linear complementarity problems are introduced in [ ]. By introducing a smooth equation and some reasonable equivalent reformulations, we investigate a generalized Newton iteration method with high-order convergence rate for solving a class of large-scale linear complementarity problem, which make full use of the superiority of the second-order convergence rate of the classical Newton method.
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