A new one-step smoothing Newton method for the second-order cone complementarity problem

作者：Fang, Liang^*; Han, Congying

来源：Mathematical Methods in the Applied Sciences, 2011, 34(3): 347-359.

DOI：10.1002/mma.1366

• second-order cone complementarity
• smoothing Newton method
• Jordan product
• coerciveness
• global convergence

In this paper, we present a new one-step smoothing Newton method for solving the second-order cone complementarity problem (SOCCP). Based on a new smoothing function, the SOCCP is approximated by a family of parameterized smooth equations. At each iteration, the proposed algorithm only need to solve one system of linear equations and perform only one Armijo-type line search. The algorithm is proved to be convergent globally and superlinearly without requiring strict complementarity at the SOCCP solution. Moreover, the algorithm has locally quadratic convergence under mild conditions. Numerical experiments demonstrate the feasibility and efficiency of the new algorithm.

• 出版日期2011-2
• 单位山东科技大学; 泰山学院