Convergence of the gradient projection method for generalized convex minimization

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	Convergence of the gradient projection method for generalized convex minimization
	Wang, CY ; Xiu, NH
	2000-07-01
发表期刊	COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
ISSN	0926-6003
卷号	16 期号:2 页码:111-120
摘要	This paper develops convergence theory of the gradient projection method by Calamai and More (Math. Programming, vol. 39, 93-116, 1987) which, for minimizing a continuously differentiable optimization problem min{f(x) : x is an element of Ohm} where Ohm is a nonempty closed convex set, generates a sequence x(k+1) = P(x(k) - alpha(k) del f(x(k))) where the stepsize alpha(k) > 0 is chosen suitably. It is shown that, when f(x) is a pseudo-convex (quasi-convex) function, this method has strong convergence results: either x(k) --> x* and x* is a minimizer (stationary point); or parallel to x(k)parallel to --> infinity arg min{f(x) : x is an element of Ohm} = empty set, and f(x(k)) down arrow inf{f(x) : x is an element of Ohm}.
关键词	generalized convex minimization gradient projection method global convergence
语种	英语
WOS研究方向	Operations Research & Management Science ; Mathematics
WOS类目	Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000088618700001
出版者	KLUWER ACADEMIC PUBL
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/15048
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, CY
作者单位	1.Acad Sinica, Inst Appl Math, Beijing 100080, Peoples R China 2.Qufu Teachers Univ, Ctr Operat Res, Qufu, Peoples R China 3.Dalian Univ Technol, Dept Appl Math, Dalian 116024, Peoples R China 4.No Jiaotong Univ, Dept Appl Math, Beijing 100044, Peoples R China
推荐引用方式 GB/T 7714	Wang, CY,Xiu, NH. Convergence of the gradient projection method for generalized convex minimization[J]. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,2000,16(2):111-120.
APA	Wang, CY,&Xiu, NH.(2000).Convergence of the gradient projection method for generalized convex minimization.COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,16(2),111-120.
MLA	Wang, CY,et al."Convergence of the gradient projection method for generalized convex minimization".COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 16.2(2000):111-120.