New convergence analysis of a class of smoothing Newton-type methods for second-order cone complementarity problem

Abstract

<abstract><p>In this paper we propose a class of smoothing Newton-type methods for solving the second-order cone complementarity problem (SOCCP). The proposed method design is based on a special regularized Chen-Harker-Kanzow-Smale (CHKS) smoothing function. When the solution set of the SOCCP is nonempty, our method has the following convergence properties: (ⅰ) it generates a bounded iteration sequence; (ⅱ) the value of the merit function converges to zero; (ⅲ) any accumulation point of the generated iteration sequence is a solution of the SOCCP; (ⅳ) it has the local quadratic convergence rate under suitable assumptions. Some numerical results are reported.</p></abstract>