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

作者：Tang, Jingyong^*; He, Guoping; Dong, Li; Fang, Liang; Zhou, Jinchuan

来源：Applications of Mathematics, 2013, 58(2): 223-247.

DOI：10.1007/s10492-013-0011-9

• second-order cone complementarity problem
• smoothing function
• smoothing Newton method
• global convergence
• quadratic convergence

In this paper we introduce a new smoothing function and show that it is coercive under suitable assumptions. Based on this new function, we propose a smoothing Newton method for solving the second-order cone complementarity problem (SOCCP). The proposed algorithm solves only one linear system of equations and performs only one line search at each iteration. It is shown that any accumulation point of the iteration sequence generated by the proposed algorithm is a solution to the SOCCP. Furthermore, we prove that the generated sequence is bounded if the solution set of the SOCCP is nonempty and bounded. Under the assumption of nonsingularity, we establish the local quadratic convergence of the algorithm without the strict complementarity condition. Numerical results indicate that the proposed algorithm is promising.

• 出版日期2013-4
• 单位信阳师范学院; 山东科技大学; 泰山学院; 山东理工大学; 上海交通大学