最大单调算子零点问题的分裂算法

The Splitting Algorithm for Finding a Root of a Maximal Monotone Operator

通过对Paul Tseng提出的分裂算法加一贯性项得到了一种对最大单调算子零点问题的修正算法,另外借鉴了解单调变分不等式中的外梯度类方法,得到了一种更易执行的算法。并且在一定条件下对改进算法的收敛性进行了证明。

Combining the inertial method with the forward-backward splitting method modified by Paul Tseng, a new modified method for finding a root of a maximal monotone operator is obtained. In addition, a more practical method of the problem is discussed in the spirit of extragradient-like method for monotone variational inequalities. The convergence of the methods under appropriate assumptions is established .