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A smoothing Newton method for the second-order cone complementarity problem |
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| Authors: | Jingyong Tang Guoping He Li Dong Liang Fang Jinchuan Zhou |
| Institution: | 1. College of Mathematics and Information Science, Xinyang Normal University, 464000, Xinyang, P.R.China 2. Department of Mathematics, Shanghai Jiaotong University, 200240, Shanghai, P.R.China 3. College of Information Science and Engineering, Shandong University of Science and Technology, 266510, Qingdao, P.R.China 4. College of Mathematics and Information Science, Xinyang Normal University, 464000, Xinyang, P.R.China 5. College of Mathematics and Systems Science, Taishan University, 271012, Tai’an, P.R.China 6. Department of Mathematics, School of Science, Shandong University of Technology, 255049, Zibo, P.R.China |
| Abstract: | 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. |
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