In this paper,we study a nonmonotone smoothing inexact Newton algorithm for solving the weighted horizontal linear complementarity problem(wHLCP).The algorithm uses a smoothing function to reformulate the wHLCP as a nonlinear system of equations and then solve it by inexact Newton's method.Since inexact directions are not necessarily descent,the algorithm adopts a new nonmonotone line search technique to ensure its globalization.Especially,we prove that the generated iteration sequence is bounded under the P-pair condition.Moreover,we analyze the local convergence rate of the algorithm under the Hölderian local error bound condition which is more general than the local error bound condition.The algorithm solves the nonlinear equations only approximately so that a lot of computation time can be saved.Numerical experiment results confirm the advantage of the algorithm.
关键词
加权水平线性互补问题/光滑算法/非精确牛顿法/非单调技术/Hölderian局部误差界
Key words
weighted horizontal linear complementarity problem/smoothing algorithm/inexact New-ton algorithm/nonmonotone technique/Hölderian local error bound
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