A nonmonotone smoothing Newton algorithm for circular cone complementarity problems

摘要

The circular cone complementarity problem (CCCP) is a particular nonsymmetric cone optimization problem, which is widely used in real engineering problems. In this paper, we first reformulate the CCCP as a nonlinear system of equations by a one-parametric class of smoothing functions, and then propose a nonmonotone smoothing Newton method for solving the CCCP. A new nonmonotone line search scheme is used in the proposed algorithm, which can help to improve the convergence speed of the algorithm and find the optimal solution more rapidly. Under suitable assumptions, the global convergence and local quadratic convergence are achieved. Finally, numerical results of the force optimization problem for a quadruped robot and random generated CCCPs illustrate the effectiveness of our new algorithm.