一种惯性邻近的Peaceman-Rachford分裂方法

发布时间：2018-03-26 21:06

本文选题：凸优化　切入点：半邻近分裂方法　出处：《中国科学:数学》2017年02期

【摘要】：严格压缩的Peaceman-Rachford(PR)分裂方法是一种收敛速度快于交替方向乘子法的求解线性约束可分离凸优化问题的有效方法.最近提出的半邻近PR分裂方法是严格压缩的PR分裂方法的一种改进方法.基于惯性邻近交替方向乘子法的思想,本文进一步改进了半邻近PR分裂方法,提出了一种惯性邻近PR分裂方法.该方法利用前两次产生的迭代点来产生新的迭代点,可以加速半邻近PR分裂方法的收敛.本文提出的方法具有一般性,它包含严格压缩的PR分裂方法和半邻近PR分裂方法作为特殊情形.在一定的假设下,本文证明了该算法产生的迭代序列的渐进可行性及函数值的收敛性,进而得到了迭代序列的全局收敛性.最后,本文通过数值试验说明了算法的有效性.
[Abstract]:The strictly contractive Peaceman-Rachfordberg splitting method is an efficient method for solving linear constrained separable convex optimization problems with linear constraints faster than the alternating direction multiplier method. The recently proposed semi-adjacent PR splitting method is a strictly compressed PR splitting method. Based on the idea of inertial proximity alternating direction multiplier method, In this paper, the semi-adjacent PR splitting method is further improved, and an inertial neighbor PR splitting method is proposed. It can accelerate the convergence of semi-adjacent PR splitting method. The method proposed in this paper is general, which includes strictly compressed PR splitting method and semi-adjacent PR splitting method as special case. In this paper, the asymptotic feasibility of the iterative sequence and the convergence of the function value are proved, and the global convergence of the iterative sequence is obtained. Finally, the validity of the algorithm is demonstrated by numerical experiments.
【作者单位】：河北工业大学理学院;河北工业大学控制科学与工程学院;
【基金】：国家自然科学基金(批准号:11271107,11671116和91630202) 河北省自然科学基金(批准号:A2015202365)资助项目
【分类号】：O221

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