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Some Remarks on the Convex Feasibility Problem and Best Approximation Problem

Some Remarks on the Convex Feasibility Problem and Best Approximation Problem
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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. 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.
出处 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 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
关键词 Convex feasibility problem best approximation problem projection method CONVERGENCE 可行性问题 近似值 投射方法 收敛函数
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  • 1Yu. Nesterov.Smooth minimization of non-smooth functions[J].Mathematical Programming.2005(1)
  • 2J. Pe?a,J. Renegar.Computing approximate solutions for convex conic systems of constraints[J].Mathematical Programming.2000(3)
  • 3Zhi-Quan Luo,Jie Sun.A Polynomial Cutting Surfaces Algorithm for the Convex Feasibility Problem Defined by Self-Concordant Inequalities[J].Computational Optimization and Applications.2000(2)
  • 4P. L. Combettes.Hilbertian convex feasibility problem: Convergence of projection methods[J].Applied Mathematics & Optimization.1997(3)
  • 5Hein Hundal,Frank Deutsch.Two generalizations of Dykstra’s cyclic projections algorithm[J].Mathematical Programming.1997(2)
  • 6Liqun Qi.Superlinearly convergent approximate Newton methods for LC1 optimization problems[J].Mathematical Programming (-).1994(1-3)
  • 7Jonathan Eckstein,Dimitri P. Bertsekas.On the Douglas—Rachford splitting method and the proximal point algorithm for maximal monotone operators[J].Mathematical Programming (-).1992(1-3)
  • 8Alfredo N. Iusem,Alvaro R. Pierro.On the convergence of Han’s method for convex programming with quadratic objective[J].Mathematical Programming (-).1991(1-3)
  • 9Krzysztof C. Kiwiel.Exact penalty functions in proximal bundle methods for constrained convex nondifferentiable minimization[J].Mathematical Programming (-).1991(1-3)
  • 10J.-P.AUBIN.Optima and Equilibria[]..1993

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