# A linearly convergent derivative-free descent method for the second-order cone complementarity problem

Shaohua Pan, Jein Shan Chen*

*此作品的通信作者

9 引文 斯高帕斯（Scopus）

## 摘要

We consider a class of derivative-free descent methods for solving the second-order cone complementarity problem (SOCCP). The algorithm is based on the Fischer-Burmeister (FB) unconstrained minimization reformulation of the SOCCP, and utilizes a convex combination of the negative partial gradients of the FB merit function FB as the search direction. We establish the global convergence results of the algorithm under monotonicity and the uniform Jordan P-property, and show that under strong monotonicity the merit function value sequence generated converges at a linear rate to zero. Particularly, the rate of convergence is dependent on the structure of second-order cones. Numerical comparisons are also made with the limited BFGS method used by Chen and Tseng (An unconstrained smooth minimization reformulation of the second-order cone complementarity problem, Math. Program. 104(2005), pp. 293-327), which confirm the theoretical results and the effectiveness of the algorithm.

原文 英語 1173-1197 25 Optimization 59 8 https://doi.org/10.1080/02331930903085359 已發佈 - 2010

• 控制和優化
• 管理科學與經營研究
• 應用數學