项目名称: 区间约束矩阵最优化问题有效算法及其应用研究
项目编号: No.11261014
项目类型: 地区科学基金项目
立项/批准年度: 2013
项目学科: 数理科学和化学
项目作者: 彭振赟
作者单位: 桂林电子科技大学
项目金额: 45万元
中文摘要: 本项目将致力研究源于金融理论、信号与图象处理、统计分析和系统控制等领域中的矩阵方程与矩阵不等式约束下元素区间约束、特征值区间约束、范数区间约束和秩区间约束矩阵最优化问题。 对矩阵方程与矩阵不等式约束下元素区间约束和特征值区间约束矩阵最优化问题。从减少算法计算量、简化算法结构的角度出发,充分利用矩阵理论和最优化理论中的有关理论和方法,设计出矩阵特殊结构特征不发生变化的、快速、稳定的计算方法。 对矩阵方程与矩阵不等式约束下范数区间约束和秩区间约束矩阵最优化问题。通过将非凸优化问题等价转化为可解凸优化问题或通过构造新的可解子问题,并对主搜索方向提出一些新的修正方法,设计出快速、稳定的,且能适应于不同问题规模的计算方法。 研究区间约束矩阵最优化问题的实际应用。建立新的扰动分析理论和预处理修正技术处理病态问题。对所设计的求解实际问题的计算方法进行有效性和可靠性分析。
中文关键词: 约束矩阵方程;最小二乘问题;迭代方法;Dykstra’s交替投影算法;交替方向算法
英文摘要: This project will studies the optimization problems with the element interval constraints matrices,the eigenvalue interval constraints matrices,the norm interval constraints matrices and the rank interval constraints matrices under the matrix equations and the matrix inequalities constraints in finance theory,signal and image processing,statistic analysis,systems control theory,and so on. For the optimization problems with the element interval constraints matrices and the eigenvalue interval constraints matrices under the matrix equations and the matrix inequalities constraints. We start from reduce the computation quantity of algorithm and simplified algorithm structure,and through the full use of the theories and the methods in the matrix theory and the optimization theory. Designed the algorithms with the matrix special structure features do not change, fast convergence and stable to solve considered problems. For the optimization problems with the norm interval constraints matrices and the rank interval constraints matrices under the matrix equations and the matrix inequalities constraints. We consider transforming the nonconvex optimization problems into the equivalent convex optimization problems or through construct some new sovable subproblems, and, for mainly search direction, present some new correcti
英文关键词: Constraints matrix equation;least squares problem;iteration method;Dykstra’s alternating projection algorithm;alternating direction algorithm