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惯性β-Douglas-Rachford分裂算法收敛性分析

Convergence Analysis of Inertial β -Douglas-Rachford Splitting Algorithm
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摘要 Douglas-Rachford分裂算法是一种求解两个极大单调算子和的零点的经典方法,一直深受广大学者的关注.针对经典Douglas-Rachford分裂算法,本文提出一种基于惯性Douglas-Rachford分裂算法的惯性β-Douglas-Rachford分裂算法,应用惯性K-M算法对惯性β-Douglas-Rachford分裂算法的收敛性进行详细分析.通过引入极大单调算子的β-增强算子给出惯性β-Douglas-Rachford分裂算法的解的形式. Douglas-Rachford splitting algorithm is a classical method for solving the zeros of the sum of two maximal monotone operators.Since it was proposed,it has attracted the attention of many scholars.Aiming at the classical Douglas-Rachford splitting algorithm,an inertialβ-Douglas-Rachford splitting algorithm based on inertial Douglas-Rachford splitting algorithm is proposed,and the convergence of inertialβ-Douglas-Rachford splitting algorithm is analyzed in detail by using inertial K-M algorithm.In addition,the solution of the inertialβ-Douglas-Rachford splitting algorithm is given by introducing theβ-enhancement operator of the maximal monotone operator.
作者 张家乐 欧阳薇 ZHANG Jia-le;OUYANG Wei(School of Mathematics,Yunnan Normal University,Kunming 650091,China)
出处 《长春师范大学学报》 2023年第6期11-18,共8页 Journal of Changchun Normal University
关键词 Douglas-Rachford分裂算法 惯性β-Douglas-Rachford分裂算法 惯性K-M算法 收敛性分析 β-增强算子 Douglas-Rachford splitting algorithm Inertialβ-Douglas-Rachford splitting algorithm Inertial K-M splitting algorithm convergence analysis β-enhancement operator
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