Related papers: A note on Douglas-Rachford, gradients, and phase r…
We propose a new approach for analyzing convergence of the Douglas-Rachford splitting method for solving convex composite optimization problems. The approach is based on a continuously differentiable function, the Douglas-Rachford Envelope…
Motivated by nonconvex, inconsistent feasibility problems in imaging, the relaxed alternating averaged reflections algorithm, or relaxed Douglas-Rachford algorithm (DR$\lambda$), was first proposed over a decade ago. Convergence results for…
In this paper, we study the generalized Douglas-Rachford algorithm and its cyclic variants which include many projection-type methods such as the classical Douglas-Rachford algorithm and the alternating projection algorithm. Specifically,…
This paper proposes an algorithm for solving structured optimization problems, which covers both the backward-backward and the Douglas-Rachford algorithms as special cases, and analyzes its convergence. The set of fixed points of the…
We present the convergence analysis of convex combination of the alternating projection and Douglas-Rachford operators for solving the phase retrieval problem. New convergence criteria for iterations generated by the algorithm are…
Douglas-Rachford Splitting (DRS) methods based on the proximal point algorithms for the Poisson and Gaussian log-likelihood functions are proposed for ptychography and phase retrieval. Fixed point analysis shows that the DRS iterated…
The Douglas-Rachford projection algorithm is an iterative method used to find a point in the intersection of closed constraint sets. The algorithm has been experimentally observed to solve various nonconvex feasibility problems which…
The Douglas-Rachford (DR) algorithm is an iterative procedure that uses sequential reflections onto convex sets and which has become popular for convex feasibility problems. In this paper we propose a structural generalization that allows…
The Douglas-Rachford algorithm (DRA) is a powerful optimization method for minimizing the sum of two convex (not necessarily smooth) functions. The vast majority of previous research dealt with the case when the sum has at least one…
Douglas-Rachford (DR) algorithm is analyzed for Fourier phase retrieval with a single random phase mask. Local, geometric convergence to a unique fixed point is proved with numerical demonstration of global convergence.
The Douglas-Rachford algorithm is a simple yet effective method for solving convex feasibility problems. However, if the underlying constraints are inconsistent, then the convergence theory is incomplete. We provide convergence results when…
We adapt the Douglas-Rachford (DR) splitting method to solve nonconvex feasibility problems by studying this method for a class of nonconvex optimization problem. While the convergence properties of the method for convex problems have been…
The Douglas-Rachford reflection method is a general purpose algorithm useful for solving the feasibility problem of finding a point in the intersection of finitely many sets. In this chapter we demonstrate that applied to a specific…
In recent years, a distributed Douglas-Rachford splitting method (DDRSM) has been proposed to tackle multi-block separable convex optimization problems. This algorithm offers relatively easier subproblems and greater efficiency for…
The Douglas-Rachford (DR) method is a widely used method for finding a point in the intersection of two closed convex sets (feasibility problem). However, the method converges weakly and the associated rate of convergence is hard to analyze…
We are interested in restoring images having values in a symmetric Hadamard manifold by minimizing a functional with a quadratic data term and a total variation like regularizing term. To solve the convex minimization problem, we extend the…
The Douglas-Rachford method, a projection algorithm designed to solve continuous optimization problems, forms the basis of a useful heuristic for solving combinatorial optimization problems. In order to successfully use the method, it is…
We study the cyclic relaxed Douglas-Rachford algorithm for possibly nonconvex, and inconsistent feasibility problems. This algorithm can be viewed as a convex relaxation between the cyclic Douglas-Rachford algorithm first introduced by…
Many large-scale and distributed optimization problems can be brought into a composite form in which the objective function is given by the sum of a smooth term and a nonsmooth regularizer. Such problems can be solved via a proximal…
Solving feasibility problems is a central task in mathematics and the applied sciences. One particularly successful method is the Douglas-Rachford algorithm. In this paper, we provide many new conditions sufficient for finite convergence.…