On the order of the operators in the Douglas-Rachford algorithm
نویسندگان
چکیده
The Douglas–Rachford algorithm is a popular method for finding zeros of sums of monotone operators. By its definition, the Douglas–Rachford operator is not symmetric with respect to the order of the two operators. In this paper we provide a systematic study of the two possible Douglas–Rachford operators. We show that the reflectors of the underlying operators act as bijections between the fixed points sets of the two Douglas–Rachford operators. Some elegant formulae arise under additional assumptions. Various examples illustrate our results. 2010 Mathematics Subject Classification: Primary 47H09, 90C25. Secondary 47H05, 49M27, 65K05.
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ورودعنوان ژورنال:
- Optimization Letters
دوره 10 شماره
صفحات -
تاریخ انتشار 2016