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This paper establishes a theoretical framework of infeasible Mehrotra-type predictor-corrector algorithm for Cartesian nonlinear complementarity problems over symmetric cones which can be regarded as an extension of Liu et al. [Polynomial convergence of Mehrotra-type predictor-corrector algorithm for the Cartesian -LCP over symmetric cones, Optimization 64(4) (2013), pp. 1-23] for Cartesian linear complementarity problems over symmetric cones to Cartesian nonlinear complementarity problems over symmetric cones. The iteration complexities of the proposed algorithm are estimated and some numerical results are provided. The numerical results show that the proposed algorithm is efficient and reliable. [ABSTRACT FROM AUTHOR]

The smoothing-type algorithm has been a powerful tool for solving various optimization problems. In order to improve the numerical results of the algorithm, the nonmonotone line search technique has been used when the algorithm is implemented. However, the theoretical analysis is based on the algorithm with some monotone line search. In this paper, based on the smoothed Kanzow-Kleinmichel NCP function, we propose a smoothing Newton algorithm for solving the nonlinear complementarity problem with a new nonmonotone line search. We show that the nonmonotone algorithm is globally and locally superlinearly convergent under suitable assumptions. The preliminary numerical results are also reported. [ABSTRACT FROM AUTHOR]