In this paper we provide a generalization of the Douglas--Rachford splitting (DRS) and the primal-dual algorithm [L. Condat, J. Optim. Theory Appl., 158 (2013), pp. 460--479; B. C. Vu͂, Adv. Comput. Math., 38 (2013), pp. 667--681] for solving monotone ...

We present a first-order quadratic cone programming algorithm that can scale to very large problem sizes and produce modest accuracy solutions quickly. Our algorithm returns primal-dual optimal solutions when available or certificates of infeasibility ...

Nowadays the Potts model works as the key model in a broad spectrum of applications in image processing and computer vision, which can be mathematically formulated in the form of min-cuts and, meanwhile, solved in terms of flow maximizing under the ...

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 sequences are always ...

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 minimizer. In the absence ...

Many imaging problems, such as total variation reconstruction of X-ray computed tomography (CT) and positron-emission tomography (PET), are solved via a convex optimization problem with near-circulant, but not actually circulant, linear systems. The ...

Although originally designed and analyzed for convex problems, the alternating direction method of multipliers (ADMM) and its close relatives, Douglas--Rachford splitting (DRS) and Peaceman--Rachford splitting (PRS), have been observed to perform ...

Primal-dual splitting schemes are a class of powerful algorithms that solve complicated monotone inclusions and convex optimization problems that are built from many simpler pieces. They decompose problems that are built from sums, linear compositions, ...

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 ...

We propose a preconditioned version of the Douglas--Rachford splitting method for solving convex-concave saddle-point problems associated with Fenchel--Rockafellar duality. Our approach makes it possible to use approximate solvers for the linear subproblem ...

In this paper we propose two different primal-dual splitting algorithms for solving inclusions involving mixtures of composite and parallel-sum type monotone operators which rely on an inexact Douglas--Rachford splitting method, but applied in different ...