凸两分块问题的两个分裂算法

发布时间：2018-02-13 19:23

本文关键词： 凸两分块优化 Peaceman-Rachford分裂算法乘子交替方向法非正定正则化收敛率　出处：《广西大学》2017年硕士论文　论文类型：学位论文

【摘要】：凸两分块优化问题广泛出现在实际应用中,如信号和图像处理、数据挖掘和分类、机器与统计学习、主成分分析、资产配置等.因此,研究凸两分块优化问题的求解算法在理论和实际应用方面都有重要的意义.乘子交替方向法(ADMM)与Peaceman-Rachford分裂算法是求解凸两分块优化问题的两类十分有效的算法.本文主要研究正则化乘子交替方向法的收敛率与非正定正则化Peaceman-Rachford分裂算法的构造与理论.具体内容如下:首先,针对凸两分块优化问题,给出了一个非正定正则化Peaceman-Rach-ford分裂算法.证明了该算法的收敛性以及在遍历意义下O(1/k)的收敛率.通过数值试验验证了算法的有效性.其次,针对凸两分块优化问题,对经典乘子交替方向法的x和y子问题均引入正则项,分析了凸两分块优化问题的正则化乘子交替方向法遍历意义下的O(1/k)收敛率.数值试验结果表明算法是有效和稳定的.
[Abstract]:Convex two-block optimization problems are widely used in practical applications, such as signal and image processing, data mining and classification, machine and statistical learning, principal component analysis, asset allocation, etc. It is very important to study the algorithms for solving convex two-block optimization problems in theory and in practice. The multiplier alternating direction method (ADMMM) and the Peaceman-Rachford splitting algorithm are two kinds of very effective algorithms for solving convex two-block optimization problems. This paper mainly studies the convergence rate of regularization multiplier alternating direction method and the construction and theory of non-positive definite regularization Peaceman-Rachford splitting algorithm. For convex two-block optimization problem, a non-positive definite regularization Peaceman-Rach-ford splitting algorithm is presented. The convergence of the algorithm and the convergence rate of OF1 / k in the sense of ergodic are proved. The validity of the algorithm is verified by numerical experiments. For convex two-block optimization problems, the canonical terms are introduced to the x and y subproblems of the classical multiplier alternating direction method. In this paper, the convergence rate of O _ (1 / 1 / k) in the sense of ergodic of regularization multiplier alternating direction method for convex two-block optimization problem is analyzed. The numerical results show that the algorithm is effective and stable.
【学位授予单位】：广西大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O224

【相似文献】