Some Remarks on the Convex Feasibility Problem and Best Approximation Problem  

作　　者：Qingzhi Yang Jinling Zhao 

机构地区：[1]School of Mathematics and LPMC, Nankai University, Tianjin 300071, China [2]School of Applied Science, University of Science and Technology, Beijing 100080, China

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2008年第1期78-91,共14页高等学校计算数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China,Grant 10571134

摘　　要：In this paper we investigate several solution algorithms for the convex fea- sibility problem(CFP)and the best approximation problem(BAP)respectively.The algorithms analyzed are already known before,but by adequately reformulating the CFP or the BAP we naturally deduce the general projection method for the CFP from well-known steepest decent method for unconstrained optimization and we also give a natural strategy of updating weight parameters.In the linear case we show the connec- tion of the two projection algorithms for the CFP and the BAP respectively.In addition, we establish the convergence of a method for the BAP under milder assumptions in the linear case.We also show by examples a Bauschke's conjecture is only partially correct.In this paper we investigate several solution algorithms for the convex feasibility problem （CFP） and the best approximation problem （BAP） respectively. The algorithms analyzed are already known before, but by adequately reformulating the CFP or the BAP we naturally deduce the general projection method for the CFP from well-known steepest decent method for unconstrained optimization and we also give a natural strategy of updating weight parameters. In the linear case we show the connection of the two projection algorithms for the CFP and the BAP respectively. In addition, we establish the convergence of a method for the BAP under milder assumptions in the linear case. We also show by examples a Bauschke＇s conjecture is only partially correct.

关 键 词：Convex feasibility problem best approximation problem projection method CONVERGENCE 

分 类 号：O24[理学—计算数学]