交替最小化算法求解一类强凸加弱凸和的收敛性  

Alternating Minimization Algorithm for“Strongly+Weakly” Convex Programming

作　　者：陈玉洁 叶明露[1] CHEN Yujie;YE Minglu(School of Mathematics and Information,China West Normal University,Nanchong Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《西华师范大学学报（自然科学版）》2020年第2期147-151,共5页Journal of China West Normal University(Natural Sciences)

基　　金：国家自然科学基金项目(11871059,11801455)。

摘　　要：利用交替最小化算法(AMA)来求解强凸加弱凸的凸组合优化问题。当强凸系数和弱凸系数满足一定关系时,通过适当选择步长,证明了AMA算法生成的点列能收敛到问题的稳定点,并且,若其中一个目标函数是光滑函数,则AMA生成的点列具有线性收敛性。The separable convex optimization problem of strongly convex function and weakly convex function is found in many practical applications.Therefore,its research has attracted much attention.In this paper,Alternating Minimization Algorithm(AMA)is used for solving the convex optimization problem of strongly convex function and weakly convex function.It is proved that the sequence generated by AMA is convergent to the stationary point of the optimization problem when strongly convex modulus and weakly convex modulus satisfy certain relations and a suitable step size is picked.Moreover,if one of the objective functions is smooth,the sequence generated by AMA shows a linear convergence.

关 键 词：交替最小化算法 强凸函数 弱凸函数 收敛 

分 类 号：O177.9[理学—数学]