Abstract:

In this paper, we propose a regularized nonmonotone inexact smoothing Newton algorithm for solving the weighted symmetric cone complementarity problem(wSCCP). In the algorithm, we consider the regularized parameter as an independent variable. Therefore, it is simpler and easier to implement than many available algorithms. At each iteration, we only need to obtain an inexact solution of a system of equations. Moreover, the nonmonotone line search technique adopted in our algorithm includes two popular nonmonotone search schemes. We prove that the algorithm is globally and locally quadratically convergent under suitable assumptions. Finally, some preliminary numerical results indicate the effectiveness of our algorithm.

Key words: Regularized inexact smoothing Newton algorithm, Weighted symmetric cone complementarity problem, Nonmonotone line search, Global convergence, Locally quadratic convergence