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学术报告

信息来源: 发布日期: 2017-03-24浏览次数:

学术报告

 

报告人:车海涛博士

报告地点:JC819

 

时间:324日下午2:00-3:00

题目: A simultaneous iterative method for split equality problems

摘要: In this article, we first introduce the concept of -mapping of a finite family of strictly pseudononspresding mapping , and we show that the fixed point set of the -mapping is the set of common fixed points of  and is a quasi-nonexpansive mapping. Based on the concept of -mapping, we propose a simultaneous iterative algorithm to solve split equality problem with a way of selecting the stepsizes which does not need any priori information about the operator norms. The sequences generated by the algorithm weakly converge to a solution of split equality problem of two finite families of strictly pseudononspresding mappings. Furthermore, we apply our iterative algorithms to some convex and nonlinear problems. Finally, several numerical results are shown to confirm the feasibility and efficiency of the proposed methods.

 

时间:325日下午2:00-3:00

题目A new iterative method for the extended split equality problem and the extended split equality fixed point problem

摘要:In this article, we first propose an extended split equality problem which is an extension of the convex feasibility problems, and then introduce a parameter w to establish the fixed point equation system. We show the equivalence of the extended split equality problem and the fixed point equation system. Based on the fixed point equation system, we propose a simultaneous iterative algorithm and obtain the weak convergence of the proposed algorithm. Further, by introducing the concept of G-mapping of a finite family of strictly pseudononspreading mapping, we consider an extended split equality fixed point problem for G-mapping and propose a simultaneous iterative algorithm with a way of selecting the stepsizes which do not need any prior information about the operator norms, and the weak convergence of the proposed algorithm is obtained. We apply our iterative algorithms to some convex and nonlinear problems. Finally, several numerical results are shown to confirm the feasibility and efficiency of the proposed methods.

车海涛,理学博士,副教授,潍坊学院数学与信息科学学院教师。2013年博士毕业于曲阜师范大学应用数学专业,目前主要从事最优化理论与算法以及偏微分方程数值方法等方面的研究,在《Applied Mathematics and Computation》、《Journal of Computational and Applied Mathematics》以及《Numerical Methods for Partial Differential Equations》等国内外学术刊物发表具有一定学术影响力的SCI论文12篇,现主持国家自然科学基金和山东省高校科技计划项目各一项。荣获山东省研究生优秀科技创新成果奖,山东省高等学校优秀科研成果奖三等奖,潍坊市自然科学奖三等奖,曲阜师范大学校长科研奖励基金,潍坊学院优秀科研成果奖一等奖各一项。现为美国《数学评论》评论员。