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迭代算法收敛性理论研究及其在图像恢复中的应用
  • 项目名称：迭代算法收敛性理论研究及其在图像恢复中的应用
  • 项目类别：面上项目
  • 批准号：11071279
  • 申请代码：A010601
  • 项目来源：国家自然科学基金
  • 研究期限：2011-01-01-2013-12-31
  • 项目负责人：陈汝栋
  • 负责人职称：教授
  • 依托单位：天津工业大学
  • 批准年度：2010
中文摘要：

分裂可行性问题和多集分裂可行性问题在图像恢复和医学上的强度可调辐射疗法中有重要的应用，而分裂可行性问题和多集分裂可行性问题的求解可归结为非线性算子不动点和零点的迭代逼近问题。本课题以图像处理技术和医学上的强度可调辐射疗法为背景，研究相关的非线性算子零点、不动点的迭代逼近算法，主要包括通过构造算法求非线性算子方程的最小范数解，并应用于解决相关的分裂可行性问题；将非扩张算子不动点的相关算法应用到特定泛函的极小值问题，解决多集分裂可行性问题；并实现相应迭代算法的计算机编程。

中文主题词： 分裂可行性；不动点；迭代逼近；非扩张映像；分裂等式
英文摘要：

split feasibility；fixed point；the iterative approximation；nonexpansive mapping；split equation

英文主题词： split feasibility；fixed point；the iterative approximation；nonexpansive mapping；split equation
结论摘要：

本项目课题组全体成员,按照项目任务书要求,进行了不懈的努力,作出了较丰富的成果.首先，针对分裂可行性问题，分裂等式问题，分裂不动点问题等开展了一系列的研究，特别是针对相关问题的迭代逼近算法得到了一批结果，发表的论文66篇被SCI检索；其次, 结合多年从事不动点理论的研究和教学，完成了专著《不动点理论及应用》，该书包含了作者和研究生们的部分研究成果；2012年在天津工业大学召开了《非线性分析与优化国际学术会议》，来自中国、以色列、韩国、加拿大、泰国，台湾和香港地区等国家和地区的一百余名学者参加了会议，会议收到学术论文五十余篇; 邀请了20余位本领域的专家学者来我校进行了学术交流，提高了我校非线性分析团队的水平和地位; 培养了姚永红、石洛宜为代表的一批青年学术骨干和10余位硕士研究生。

成果综合统计
成果类型
数量
  • 期刊论文
  • 会议论文
  • 专利
  • 获奖
  • 著作
  • 46
  • 1
  • 0
  • 0
  • 1
期刊论文
Fixed Points of Asymptotic Pointwise Nonexpansive Mappings in Modular Spaces
Strong Convergence Theorems for a Common Fixed Point of Two Countable Families of Relatively Quasi N
Approximate Iteration Algorithm with Error Estimate for Fixed Point of Nonexpansive
Modified Hybrid Block Iterative Algorithm for Uniformly Quasi-φ-Asymptotically
Duality Fixed Point and Zero Point Theorems and Applications
On the Weak Relatively Nonexpansive Multivalued Mappings in Banach Spaces
A DUALITY FIXED POINT THEOREM AND APPLICATIONS
COUPLING EXTRA-GRADIENT METHODS WITH KM'S METHODS FOR VARIATIONAL INEQUALITIES AND FIXED POINTS
IMPLICIT AND EXPLICIT ALGORITHMS FOR MINIMUM-NORM FIXED POINTS OF PSEUDOCONTRACTIONS IN HILBERT SPAC
Algorithmic Approach to a Minimization
A MODIFIED EXTRAGRADIENT METHOD FOR THE SPLIT FEASIBILITY AND FIXED POINT PROBLEMS
Regularized Methods for the Split Feasibility Problem
HIERARCHICAL CONVERGENCE TO THE ZERO POINT OF MAXIMAL MONOTONE OPERATORS
A Regularized Gradient Projection Method for the Minimization Problem
IMPLICIT AND EXPLICIT METHODS FOR FINDING FIXED POINTS OF STRICTLY PSEUDO-CONTRACTIVE MAPPINGS IN BA
Applications of Fixed-Point and Optimization Methods to the Multiple-Set Split Feasibility Problem
Hybrid methods for accretive variational inequalities involving pseudocontractions in Banach spaces
AN EXPLICIT ITERATIVE METHOD FOR FINDING A COMMON SOLUTION OF EQUILIBRIUM AND FIXED POINT PROBLEMS
Mann Type Implicit Iteration Approximation for Multivalued Mappings in Banach Spaces
Strong convergence theorems for the implicit iteration process for a finite family of hemicontractiv
Hybrid Algorithm of Fixed Point for Weak Relatively Nonexpansive Multivalued Mappings and Applicatio
希尔伯特空间中非扩张映像的修改的Mann迭代格式的强收敛性
Banach空间中的非扩张半群的修正的Mann迭代
Hilbert空间中的可数严格伪压缩均衡问题的强弱收敛定理
Strong Convergence of Viscosity Approximation Methods for Nonexpansive Mappings in CAT(0) Spaces
Iterative Schemes for Fixed Point Computation of Nonexpansive Mappings
A unified implicit algorithm for solving the triple-hierarchical constrained optimization problem
Regularized algorithms for hierarchical fixed-point problems
Hybrid Algorithms of Nonexpansive Semigroups for Variational Inequalities
Weak and Strong Convergence Theorems for Equilibrium Problems and Countable Strict Pseudocontraction
Strong convergence theorems for a semigroup of nonexpansive mappings in Banach spaces
CONSTRUCTION OF ITERATIVE METHODS FOR VARIATIONAL INEQUALITY AND FIXED POINT PROBLEMS
Strong convergence of a proximal point algorithm with general errors
Schemes for finding minimum-norm solutions of variational inequalities
Modified Mann Iterations for Nonexpansive Semigroups in Banach Space
Variant Gradient Projection Methods for the Minimization Problems
Applications of Fixed Point and Approximate Algorithms
？ositive eigenvalue-eigenvector of lonlinear positive mappings
Affine algorithms for the split variational inequality and equilibrium problems
Regularization Method for the Approximate Split Equality Problem in Infinite-Dimensional Hilbert Spa
Delta-Convergence Problems for Asymptotically Nonexpansive Mappings in CAT(0) Spaces
An improved method for solving multiple-sets split feasibility problem
Self-Adaptive and Relaxed Self-Adaptive Projection Methods for Solving the Multiple-Set Split Feasib
On the Strong Convergence of an Algorithm about Firmly Pseudo-Demicontractive Mappings for the Split
会议论文
REGULARIZATION AND ITERATION METHODS FOR A CLASS OF MONOTONE VARIATIONAL INEQUALITIES
著作
不动点理论及应用
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