Abstract: 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.

Key words: weighted horizontal linear complementarity problem, smoothing algorithm, inexact Newton algorithm, nonmonotone technique, Hölderian local error bound