| EXTENSION OF SMOOTHING FUNCTIONS TO SYMMETRIC CONE COMPLEMENTARITY PROBLEMS |
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| 引用本文： | Liu Yongjin Zhang Liwei Liu Meijiao. EXTENSION OF SMOOTHING FUNCTIONS TO SYMMETRIC CONE COMPLEMENTARITY PROBLEMS[J]. 高校应用数学学报(英文版), 2007, 22(2): 245-252. DOI: 10.1007/s11766-007-0214-5 |
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| 作者姓名： | Liu Yongjin Zhang Liwei Liu Meijiao |
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| 作者单位： | [1]Department of Mathematics, Shantou University, Shantou 515063, China [2]Department of Applied Mathematics, Dalian University of Technology, Dalian 116023, China [3]Department of Mathematics and Physics, Dalian Jiaotong University, Dalian 116028, China |
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| 摘 要： | The paper uses Euclidean Jordan algebras as a basic tool to extend smoothing functions, which include the Chen-Mangasarian class and the Fischer-Burmeister smoothing functions, to symmetric cone complementarity problems. Computable formulas for these functions and their Jacobians are derived. In addition, it is shown that these functions are Lipschitz continuous with respect to parameter # and continuously differentiable on J × J for any μ 〉 0.
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| 关 键 词： | 光滑函数 扩张 对称锥互补问题 欧几里得约当代数 |
| 修稿时间： | 2006-03-04 |
Extension of smoothing functions to symmetric cone complementarity problems |
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| Liu Yongjin,Zhang Liwei,Liu Meijiao. Extension of smoothing functions to symmetric cone complementarity problems[J]. Applied Mathematics A Journal of Chinese Universities, 2007, 22(2): 245-252. DOI: 10.1007/s11766-007-0214-5 |
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| Authors: | Liu Yongjin Zhang Liwei Liu Meijiao |
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| Affiliation: | (1) Department of Mathematics, Shantou University, Shantou, 515063, China;(2) Department of Applied Mathematics, Dalian University of Technology, Dalian, 116023, China;(3) Department of Mathematics and Physics, Dalian Jiaotong University, Dalian, 116028, China |
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| Abstract: | The paper uses Euclidean Jordan algebras as a basic tool to extend smoothing functions, which include the Chen-Mangasarian class and the Fischer-Burmeister smoothing functions, to symmetric cone complementarity problems. Computable formulas for these functions and their Jacobians are derived. In addition, it is shown that these functions are Lipschitz continuous with respect to parameter μ and continuously differentiable on J × J for anyμ＞ 0. |
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| Keywords: | symmetric cone complementarity problem smoothing function Euclidean Jordan algebra non-interior continuation method |
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