从变分不等式的投影收缩算法到凸优化的分裂收缩算法  

FROM THE PROJECTION AND CONTRACTION METHODS FOR VARIATIONAL INEQUALITIES TO THE SPLITTING CONTRACTION METHODS FOR CONVEX OPTIMIZATION

作　　者：何炳生[1] 

机构地区：[1]南京大学数学系,南京210093

出　　处：《高等学校计算数学学报》2016年第1期74-96,共23页Numerical Mathematics A Journal of Chinese Universities

摘　　要：1引言由于互补问题(变分不等式的一种特殊情形)能用来描述经济与管理方面的平衡问题,我们对变分不等式的求解给予了极大关注.实际生活中的问题,函数只是一种对应关系,通常没有显式表达式,对一个给定的点,要获得相应的函数值叉往往要通过一次实验,代价不菲.求解这种"黑箱函数"的问题,需要只用函数值且少用函数值的方法.从管理科学中来的变分不等式问题,函数往往是黑箱的.受华罗庚先生推广优选法的影响。In the recent years, we published some splitting contraction methods for linear constrained convex optimization. These methods are effectively applied to solve the optimization problems arising from image processing, machine learning and other applied computation areas. The approach is well recognized by the scien- tific researchers. In practice, the results of splitting contraction methods are close related to the previous research work on the projection and contraction methods for monotone variational inequalities. In this paper, we give an overview on this research process. The only mathematical background required this paper is the basic concepts of calculus and linear algebra.

关 键 词：variational inequality projection and contraction methods convex optimization splitting contraction methods 

分 类 号：O221.2[理学—运筹学与控制论] O224[理学—数学]