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UBC Theses and Dissertations

A parameterized Douglas-Rachford algorithm : theory and applications Wang, Dongying


Douglas-Rachford algorithm is important due to its applications on the Heron problem and on the image denoising. Mathematically, it can be considered as finding a point such that the point belongs to a zero set of the sum of two maximally monotone operators. In this thesis, previous work on Douglas-Rachford algorithm is presented and the Douglas-Rachford algorithm with a changed parameter is considered. I give it the name "α-Douglas-Rachford algorithm". The new algorithm which has the changed parameter is shown to have a convergent result and other conclusions similar to those of the classic Douglas-Rachford algorithm. At the same time, it has been shown that the application of the α-Douglas-Rachford algorithm is wider than the application of the classic one. Later on, the α-Douglas-Rachford algorithm is proved to converge to the solution of the composited monotone inclusion problems, and in a special-limit case, it has some other properties. The numerical experiments confirm that the α-Douglas-Rachford algorithm does have the properties that I proved theoretically.

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