摘要
交替方向乘子法(ADMM)是求解大规模优化问题和非凸非光滑问题的一种有效的方法,但当目标函数为非凸非光滑的情况时,原始ADMM算法的收敛性无法保证,且若目标函数中存在耦合函数,则算法的收敛性证明将更为复杂。在现实生活中存在的很多问题,其本质都是非凸的。因此,本文提出了一种改进的ADMM算法。与原始ADMM算法相比,该算法引入了一个松弛因子α,构造了一种广义交替方向乘子法(GADMM)来求解具有线性约束的非凸不可分离优化问题。在一定的假设条件下,通过假设增广拉格朗日函数满足K-L不等式,证明了当惩罚参数足够大时,算法生成的序列收敛到增广拉格朗日函数的稳定点。
The alternating direction method of multiplies(ADMM) is an effective method for solving large-scale optimization and nonconvex non-smooth objective. However, the convergence cannot be guaranteed when the objective function is nonconvex and non-smooth. Moreover, the proof of the convergence is more complex when the objective contains coupled function. Many problems in real life are nonconvex in nature, so the research on nonconvex optimization problems is particularly important.Therefore, an improved ADMM algorithm is proposed in this paper. Compared with the original ADMM algorithm, a relaxation factor α is introduced and a generalized alternating direction multiplier method(GADMM) is constructed to solve the non-convex nonseparable optimization problem with linear constraints. Under certain assumptions, by assuming that the augmented Lagrangian function satisfies the K-L inequality, it is proved that the sequence generated by the algorithm converges to the critical point of the augmented Lagrangian function when the penalty parameter is sufficiently large.
作者
薛中会
胡惠晴
党亚峥
XUE Zhonghui;HU Huiqing;DANG Yazheng(Shanghai Publishing and Printing College,Shanghai 200093,China;Business School,University of Shanghai for Science and Technology,Shanghai 200093,China)
出处
《上海理工大学学报》
CAS
CSCD
北大核心
2021年第6期580-588,共9页
Journal of University of Shanghai For Science and Technology
基金
国家自然科学基金资助项目(72071130)。
关键词
广义交替方向乘子法
K-L不等式
非凸最优化
不可分离问题
收敛性分析
generalized alternating direction multiplier method
K-L inequality
nonconvex optimization
nonseparable problem
convergence analysis
