Global ETD Search

1	Averaged mappings and it's applications Liang, Wei-Jie 29 June 2010 (has links) A sequence fxng generates by the formula x_{n+1} =(1- £\\_n)x_n+ £\\_nT_nx_n is called the Krasnosel'skii-Mann algorithm, where {£\\_n} is a sequence in (0,1) and {T_n} is a sequence of nonexpansive mappings. We introduce KM algorithm and prove that the sequence fxng generated by KM algorithm converges weakly. This result is used to solve the split feasibility problem which is to find a point x with the property that x ∈ C and Ax ∈ Q, where C and Q are closed convex subsets form H1 to H2, respectively, and A is a bounded linear operator form H1 to H2. The purpose of this paper is to present some results which apply KM algorithm to solve the split feasibility problem, the multiple-set split feasibility problem and other applications. split feasibility problem weak convergence multiple-set split feasibility problem Krasnosel'skii-Mann algorithm averaged mapping nonexpansive mapping
2	Inverse strongly monotone operators and variational inequalities Chi, Wen-te 23 June 2009 (has links) In this paper, we report existing convergence results on monotone variational inequalities where the governing monotone operators are either strongly monotone or inverse strongly monotone. We reformulate the variational inequality problem as an equivalent fixed point problem and then use fixed point iteration method to solve the original variational inequality problem. In the case of strong monotonicity case we use the Banach¡¦s contraction principle to define out iteration sequence; while in the case of inverse strong monotonicity we use the technique of averaged mappings to define our iteration sequence. In both cases we prove strong convergence for our iteration methods. An application to a minimization problem is also included. convergence iteration projection minimization Lipschitzian operator Variational inequality inverse strongly monotone averaged mapping strongly monotone monotone fixed point
3	Iterative Approaches to the Split Feasibility Problem Chien, Yin-ting 23 June 2009 (has links) In this paper we discuss iterative algorithms for solving the split feasibility problem (SFP). We study the CQ algorithm from two approaches: one is an optimization approach and the other is a fixed point approach. We prove its convergence first as the gradient-projection algorithm and secondly as a fixed point algorithm. We also study a relaxed CQ algorithm in the case where the sets C and Q are level sets of convex functions. In such case we present a convergence theorem and provide a different and much simpler proof compared with that of Yang [7]. firmly nonexpansive mapping relaxed CQ algorithm. CQ algorithm gradient projectionalgorithm projection averaged mapping Split feasibility problem inverse strongly monotone operator

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