Related papers: A Parallel Douglas Rachford Algorithm for Minimizi…
We consider resolvent splitting algorithms for finding a zero of the sum of finitely many maximally monotone operators. The standard approach to solving this type of problem involves reformulating as a two-operator problem in the…
The Douglas-Rachford method is a popular splitting technique for finding a zero of the sum of two subdifferential operators of proper closed convex functions; more generally two maximally monotone operators. Recent results concerned with…
Recently, it has become evident that submodularity naturally captures widely occurring concepts in machine learning, signal processing and computer vision. Consequently, there is need for efficient optimization procedures for submodular…
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…
This work is concerned with the convergence rate analysis of the Douglas-Rachford splitting (DRS) method for finding a zero of the sum of two maximally monotone operators. We obtain an exact rate of convergence for the DRS algorithm and…
Douglas-Rachford splitting and its equivalent dual formulation ADMM are widely used iterative methods in composite optimization problems arising in control and machine learning applications. The performance of these algorithms depends on…
This paper introduces the distributed Halpern Peaceman--Rachford (dHPR) method, an efficient algorithm for solving distributed convex composite optimization problems with non-smooth objectives, which achieves a non-ergodic $O(1/k)$…
The Douglas--Rachford algorithm is a popular algorithm for solving both convex and nonconvex feasibility problems. While its behaviour is settled in the convex inconsistent case, the general nonconvex inconsistent case is far from being…
This paper considers constrained linear dynamic games with quadratic objective functions, which can be cast as affine variational inequalities. By leveraging the problem structure, we apply the Douglas-Rachford splitting, which generates a…
Based on the ideas of arXiv:1710.06612, we consider the problem of minimization of the Holder-continuous non-smooth functional $f$ with non-positive convex (generally, non-smooth) Lipschitz-continuous functional constraint. We propose some…
These notes focus on the minimization of convex functionals using first-order optimization methods, which are fundamental in many areas of applied mathematics and engineering. The primary goal of this document is to introduce and analyze…
The Douglas-Rachford algorithm is a very popular splitting technique for finding a zero of the sum of two maximally monotone operators. However, the behaviour of the algorithm remains mysterious in the general inconsistent case, i.e., when…
We consider finite Markov decision processes (MDPs) with convex constraints and known dynamics. In principle, this problem is amenable to off-the-shelf convex optimization solvers, but typically this approach suffers from poor scalability.…
We introduce a new convex optimization problem, termed quadratic decomposable submodular function minimization. The problem is closely related to decomposable submodular function minimization and arises in many learning on graphs and…
In recent times the Douglas-Rachford algorithm has been observed empirically to solve a variety of nonconvex feasibility problems including those of a combinatorial nature. For many of these problems current theory is not sufficient to…
The difference-of-convex (DC) program is an important model in nonconvex optimization due to its structure, which encompasses a wide range of practical applications. In this paper, we aim to tackle a generalized class of DC programs, where…
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…
We provide new insight into the convergence properties of the Douglas-Rachford algorithm for the problem $\min_x \{f(x)+g(x)\}$, where $f$ and $g$ are convex functions. Our approach relies on and highlights the natural primal-dual symmetry…
The subgradient method is a classical and foundational approach in non-smooth convex optimization; its simplicity, robustness, and role as a conceptual and algorithmic starting point have made it the backbone of many significant…
In this paper some adaptive mirror descent algorithms for problems of minimization convex objective functional with several convex Lipschitz (generally, non-smooth) functional constraints are considered. It is shown that the methods are…