A REGULARIZED INEXACT SMOOTHING NEWTON METHOD FOR CIRCULAR CONE COMPLEMENTARITY PROBLEM

In this paper, we show that the regularized Fischer-Burmeister smoothing function is coercive under suitable assumptions, which plays an important role in the global convergence of our algorithm. Consequently, we develop a regularized inexact smoothing Newton algorithm for solving the circular cone complementarity problem (CCCP) via the regularized Fischer-Burmeister smoothing function. In addition, in our algorithm, the regularized parameter is viewed as an independent variable so that it is simpler and more easily implemented than many existing algorithms. Also, our algorithm solves only one linear system of equations approximately and performs only one line search at each iteration. Moreover, our algorithm is shown to possess global and local quadratic convergence properties without strict complementarity. Finally, some numerical results illustrate the effectiveness of our algorithm for solving the CCCP.