| Some Remarks on the Convex Feasibility Problem and Best Approximation Problem |
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| 作者单位： | 1，* |
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| 基金项目： | 国家自然科学基金，University of Minnesota |
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| 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.
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| 关 键 词： | 可行性问题 近似值 投射方法 收敛函数 |
Some Remarks on the Convex Feasibility Problem and Best Approximation Problem |
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| Authors: | Qingzhi Yang Jinling Zhao |
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| Institution: | 1. School of Mathematics and LPMC, Nankai University, Tianjin 300071, China
2. School of Applied Science, University of Science and Technology, Beijing 100080,China |
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| Abstract: | 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. |
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| Keywords: | Convex feasibility problem best approximation problem projection method conver-gence |
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