PROPERTIES OF A CLASS OF NONLINEAR TRANSFORMATIONS OVER EUCLIDEAN JORDAN ALGEBRAS WITH APPLICATIONS TO COMPLEMENTARITY PROBLEMS

doi:10.1080/01630560903123304

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	PROPERTIES OF A CLASS OF NONLINEAR TRANSFORMATIONS OVER EUCLIDEAN JORDAN ALGEBRAS WITH APPLICATIONS TO COMPLEMENTARITY PROBLEMS
	Lu, Nan 1; Huang, Zheng-Hai 1; Han, Jiye 2
	2009
发表期刊	NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
ISSN	0163-0563
卷号	30 期号:7-8 页码:799-821
摘要	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.
关键词	Euclidean Jordan algebra Relaxation transformation Smoothing algorithm Symmetric cone complementarity problem
DOI	10.1080/01630560903123304
语种	英语
资助项目	National Natural Science Foundation of China[10871144] ; National Natural Science Foundation of China[10671010] ; Natural Science Foundation of Tianjin[07JCYBJC05200]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000270333000008
出版者	TAYLOR & FRANCIS INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/8623
专题	中国科学院数学与系统科学研究院
通讯作者	Huang, Zheng-Hai
作者单位	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
推荐引用方式 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.