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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 PublicationNUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
ISSN0163-0563
Volume30Issue:7-8Pages:799-821
AbstractFor 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.
KeywordEuclidean Jordan algebra Relaxation transformation Smoothing algorithm Symmetric cone complementarity problem
DOI10.1080/01630560903123304
Language英语
Funding ProjectNational Natural Science Foundation of China[10871144] ; National Natural Science Foundation of China[10671010] ; Natural Science Foundation of Tianjin[07JCYBJC05200]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000270333000008
PublisherTAYLOR & FRANCIS INC
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/8623
Collection中国科学院数学与系统科学研究院
Corresponding AuthorHuang, Zheng-Hai
Affiliation1.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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