凸可行问题的松弛投影算法及其应用研究

项目名称： 凸可行问题的松弛投影算法及其应用研究

项目编号： No.11271226

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 屈彪

作者单位： 曲阜师范大学

项目金额： 67万元

中文摘要： 凸可行问题是一类常见而又重要的数学问题，有着极强的应用背景，在现代物理、医学、信号处理、图像重建、博弈论等领域中都有着广泛的应用. 因此，对凸可行问题设计有效的算法，具有重要的理论意义与显著的应用价值. 本项目就是对求解凸可行问题的松弛投影算法进行系统和深入的研究. 具体研究内容是：(1) 凸可行问题的理论分析，包括再生形式、解的结构、解的特征等；(2)构造易于投影的投影区域(集合)，建立求解凸可行问题的可行有效的松弛投影新算法，特别是具有快速收敛的有效新算法，并进行算法的理论分析；(3)收集信号处理、图像重建和博弈论中的典型实例，对它们进行模型分析，并尝试应用新算法求解. 编制数值算法程序.

中文关键词： 凸可行问题；松弛投影算法；理论分析；应用；

英文摘要： The convex feasibility problem (CFP) is a common and important class of mathematical problems, which has a very strong application background and has a wide range of applications in the field of modern physics, medical, signal processing, image reconstruction, game theory and so on. Therefore, it has important theoretical significance and notable value to design effective algorithms for the convex feasibility problem. This project is to give a systematic and in-depth study of relaxed projection algorithm for solving the convex feasibility problem. It has the following specific research contents: (1)theoretical analysis of the convex feasibility problem, including the regeneration form, the structure and features of solutions; (2) to construct the new projection region or set which is easy to projection and establish some new feasible effective relaxation projection algorithms for solving the convex feasible problem, especially the effective new algorithms with fast convergence, and give theoretical analysis for the algorithms presented in this project mentioned above; (3) collect some typical instances in signal processing, image reconstruction and game theory and give model analysis for these instances. Then attempt to solve these problems by the new algorithms proposed in this project and try to design some

英文关键词： Convex feasibility problem；Relaxed projection method；Theoretical analysis；Applications；