KMS Of Academy of mathematics and systems sciences, CAS
| PROPERTIES OF A CLASS OF NONLINEAR TRANSFORMATIONS OVER EUCLIDEAN JORDAN ALGEBRAS WITH APPLICATIONS TO COMPLEMENTARITY PROBLEMS | |
| Lu, Nan1; Huang, Zheng-Hai1; Han, Jiye2 | |
| 2009 | |
| Source Publication | NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
 |
| ISSN | 0163-0563 |
| Volume | 30Issue:7-8Pages:799-821 |
| Abstract | For any function phi from R(r) to R(r), Tao and Gowda [Math. Oper. Res., 30 (2005), pp. 985-1004] introduced a corresponding nonlinear transformation R(phi) over a Euclidean Jordan algebra (which is called a relaxation transformation) and established some useful relations between phi and R(phi). In this paper, we further investigate some interconnections between properties of phi and properties of R(phi), including the properties of continuity, (local) Lipschitz continuity, directional differentiability, (continuous) differentiability, semismoothness, monotonicity, the P(0)-property, and the uniform P-property. As an application, we investigate the symmetric cone complementarity problem with a relaxation transformation. A property of the solution set of this class of problems is given. We also investigate a smoothing algorithm for solving this class of problems and show that the algorithm is globally convergent under an assumption that the solution set of the problem concerned is nonempty. |
| Keyword | Euclidean Jordan algebra Relaxation transformation Smoothing algorithm Symmetric cone complementarity problem |
| DOI | 10.1080/01630560903123304 |
| Language | 英语 |
| Funding Project | National Natural Science Foundation of China[10871144] ; National Natural Science Foundation of China[10671010] ; Natural Science Foundation of Tianjin[07JCYBJC05200] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000270333000008 |
| Publisher | TAYLOR & FRANCIS INC |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/8623 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Huang, Zheng-Hai |
| Affiliation | 1.Tianjin Univ, Sch Sci, Dept Math, Tianjin 300072, Peoples R China 2.Chinese Acad Sci, Inst Appl Math Acad Math & Syst Sci, Beijing, Peoples R China |
| Recommended Citation GB/T 7714 | Lu, Nan,Huang, Zheng-Hai,Han, Jiye. PROPERTIES OF A CLASS OF NONLINEAR TRANSFORMATIONS OVER EUCLIDEAN JORDAN ALGEBRAS WITH APPLICATIONS TO COMPLEMENTARITY PROBLEMS[J]. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION,2009,30(7-8):799-821. |
| APA | Lu, Nan,Huang, Zheng-Hai,&Han, Jiye.(2009).PROPERTIES OF A CLASS OF NONLINEAR TRANSFORMATIONS OVER EUCLIDEAN JORDAN ALGEBRAS WITH APPLICATIONS TO COMPLEMENTARITY PROBLEMS.NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION,30(7-8),799-821. |
| MLA | Lu, Nan,et al."PROPERTIES OF A CLASS OF NONLINEAR TRANSFORMATIONS OVER EUCLIDEAN JORDAN ALGEBRAS WITH APPLICATIONS TO COMPLEMENTARITY PROBLEMS".NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION 30.7-8(2009):799-821. |
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