On convergence rate of the Douglas-Rachford operator splitting method
نویسندگان
چکیده
This note provides a simple proof on a O(1/k) convergence rate for the DouglasRachford operator splitting method where k denotes the iteration counter.
منابع مشابه
A Douglas-Rachford splitting for semi-decentralized generalized Nash equilibrium seeking in Monotone Aggregative Games
We address the generalized Nash equilibrium seeking problem for noncooperative agents playing non-strictly monotone aggregative games with affine coupling constraints. First, we use operator theory to characterize the generalized Nash equilibria of the game as the zeros of a monotone setvalued operator. Then, we massage the Douglas–Rachford splitting to solve the monotone inclusion problem and ...
متن کاملMetric Selection in Douglas-Rachford Splitting and ADMM
Recently, several convergence rate results for Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) have been presented in the literature. In this paper, we show linear convergence of Douglas-Rachford splitting and ADMM under certain assumptions. We also show that the provided bounds on the linear convergence rates generalize and/or improve on similar bounds in ...
متن کاملConvergence Rate Analysis of the Forward-Douglas-Rachford Splitting Scheme
Operator splitting schemes are a class of powerful algorithms that solve complicated monotone inclusion and convex optimization problems that are built from many simpler pieces. They give rise to algorithms in which all simple pieces of the decomposition are processed individually. This leads to easily implementable and highly parallelizable or distributed algorithms, which often obtain nearly ...
متن کاملOn the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators
This paper shows, by means of a new type of operator called a splitting operator, that the Douglas-Rachford splitting method for finding a zero of the sum of two monotone operators is a special case of the proximal point algorithm. Therefore, applications of Douglas-Rachford splitting, such as the alternating direction method of multipliers for convex programming decomposition, are also special...
متن کاملStochastic Forward Douglas-Rachford Splitting for Monotone Inclusions
We propose a stochastic Forward Douglas-Rachford Splitting framework for finding a zero point of the sum of three maximally monotone operators in real separable Hilbert space, where one of them is cocoercive. We first prove the weak almost sure convergence of the proposed method. We then characterize the rate of convergence in expectation in the case of strongly monotone operators. Finally, we ...
متن کامل