In this paper we study through iterative methods the minimization problem
min_{x∈C} £K(x) (P)
where the set C of constraints is the set of fixed points of a nonexpansive mapping T in a real Hilbert space H, and the objective function £K:H¡÷R is supposed to be continuously Gateaux dierentiable. The gradient projection method for solving problem (P) involves with the projection P_{C}. When C = Fix(T), we provide a
so-called hybrid iterative method for solving (P) and the method involves with the mapping T only. Two special cases are included: (1) £K(x)=(1/2)||x-u||^2 and (2) £K(x)=<Ax,x> - <x,b>. The first case corresponds to finding a fixed point of T which is closest to u from the fixed point set Fix(T). Both cases have received a lot of investigations recently.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0602111-000058 |
| Date | 02 June 2011 |
| Creators | Chen, Yen-Ling |
| Contributors | Jen-Chih Yao, Ngai-Ching Wong, Hong-Kun Xu, Lai-Jiu Lin |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0602111-000058 |
| Rights | unrestricted, Copyright information available at source archive |
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