三步投影算法的收敛性及其在变分不等式组中的应用

数学季刊 ›› 2009, Vol. 24 ›› Issue (2): 239-243.

三步投影算法的收敛性及其在变分不等式组中的应用

1. School of Management, Fudan University2. Group of Mathematics, Huidong Middle School of Sichuan Province

收稿日期:2005-11-21 出版日期:2009-06-30 发布日期:2023-07-21
作者简介:LUO Hong-lin(1982-), male, native of Chongqing, Ph.D., engages in optinrization theory and algorithm; LUO Hui-lin(1978-), male, native of Chongqing, engages in secondary education in Hui-dong Middle School.
基金资助:

General Convergence Analysis for Three-step Projection Methods and Applications to Variational Problems

1. School of Management, Fudan University2. Group of Mathematics, Huidong Middle School of Sichuan Province

Received:2005-11-21 Online:2009-06-30 Published:2023-07-21
About author:LUO Hong-lin(1982-), male, native of Chongqing, Ph.D., engages in optinrization theory and algorithm; LUO Hui-lin(1978-), male, native of Chongqing, engages in secondary education in Hui-dong Middle School.

摘要/Abstract

摘要： First a general model for a three-step projection method is introduced, and second it has been applied to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setting. Let H be a real Hilbert space and K be a nonempty closed convex subset of H. For arbitrarily chosen initial points x₀,y₀,z₀∈ K, compute sequences x_n,y_n,z_n such that ... . For η,ρ,γ > 0 are constants,{α_n},{β_n},{a_n},{r_n},{δ_n},{λ_n} - [0,1], {u_n},{v_n},{ω_n} are sequences in K, and 0 ≤α_n+r_n ≤ 1,0 ≤β_n+δ_n≤ 1,0 ≤ a_n+λ_n≤ 1,-n ≥ 0, where T : K → H is a nonlinear mapping onto K. At last three-step models are applied to some variational inequality problems.

关键词: two-step model, general three-step model, system of strongly monotonic nonlinear variational inequalities, projection formulas, convergence of three-projection method

Abstract: First a general model for a three-step projection method is introduced, and second it has been applied to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setting. Let H be a real Hilbert space and K be a nonempty closed convex subset of H. For arbitrarily chosen initial points x₀,y₀,z₀∈ K, compute sequences x_n,y_n,z_n such that ... . For η,ρ,γ > 0 are constants,{α_n},{β_n},{a_n},{r_n},{δ_n},{λ_n} - [0,1], {u_n},{v_n},{ω_n} are sequences in K, and 0 ≤α_n+r_n ≤ 1,0 ≤β_n+δ_n≤ 1,0 ≤ a_n+λ_n≤ 1,-n ≥ 0, where T : K → H is a nonlinear mapping onto K. At last three-step models are applied to some variational inequality problems.

Key words: two-step model, general three-step model, system of strongly monotonic nonlinear variational inequalities, projection formulas, convergence of three-projection method

中图分类号:

TP391.41

罗洪林, 罗慧林. 三步投影算法的收敛性及其在变分不等式组中的应用[J]. 数学季刊, 2009, 24(2): 239-243.

LUO Hong-lin, LUO Hui-lin. General Convergence Analysis for Three-step Projection Methods and Applications to Variational Problems [J]. Chinese Quarterly Journal of Mathematics, 2009, 24(2): 239-243.

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