A new one‐step smoothing newton method for the second‐order cone complementarity problem |
| |
Authors: | Liang Fang Congying Han |
| |
Institution: | 1. College of Mathematics and System Science, Taishan University, 271021 Tai'an, People's Republic of China;2. College of Information Science and Engineering, Shandong University of Science and Technology, 266510 Qingdao, People's Republic of China |
| |
Abstract: | 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. Copyright © 2010 John Wiley & Sons, Ltd. |
| |
Keywords: | second‐order cone complementarity smoothing Newton method Jordan product coerciveness global convergence |
|
|