相关论文: Circumcentered methods induced by isometries
We consider distributed optimization with smooth convex objective functions defined on an undirected connected graph. Inspired by mirror descent mehod and RLC circuits, we propose a novel distributed mirror descent method. Compared with…
The Douglas-Rachford algorithm is widely used in sparse signal processing for minimizing a sum of two convex functions. In this paper, we consider the case where one of the functions is weakly convex but the other is strongly convex so that…
This short tutorial presents several ideas for designing dual function radar communication (DFRC) systems aided by intelligent reflecting surfaces (IRS). These problems are highly nonlinear in the IRS parameter matrix, and further, the IRS…
Convex optimization has become ubiquitous in most quantitative disciplines of science, including variational image processing. Proximal splitting algorithms are becoming popular to solve such structured convex optimization problems. Within…
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…
Information geometry applies concepts in differential geometry to probability and statistics and is especially useful for parameter estimation in exponential families where parameters are known to lie on a Riemannian manifold. Connections…
Recently, heuristics based on the Douglas-Rachford splitting algorithm and the alternating direction method of multipliers (ADMM) have found empirical success in minimizing convex functions over nonconvex sets, but not much has been done to…
We prove that the sequences generate by the Douglas-Rachford method converge weakly to a solution of the inclusion problem
The primal-dual Douglas-Rachford method is a well-known algorithm to solve optimization problems written as convex-concave saddle-point problems. Each iteration involves solving a linear system involving a linear operator and its adjoint.…
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…
Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…
We establish finite convergence of circumcentered-reflection method (CRM) for the case of intersection of two closed convex cones in a real Hilbert space. We apply this result to prove the finite convergence for two polyhedral sets in R^n.
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…
We study acceleration and preconditioning strategies for a class of Douglas-Rachford methods aiming at the solution of convex-concave saddle-point problems associated with Fenchel-Rockafellar duality. While the basic iteration converges…
The Douglas--Rachford algorithm is a classical and very successful splitting method for finding the zeros of the sums of monotone operators. When the underlying operators are normal cone operators, the algorithm solves a convex feasibility…
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 Douglas--Rachford method is a splitting method frequently employed for finding zeroes of sums of maximally monotone operators. When the operators in question are normal cones operators, the iterated process may be used to solve…
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 the simple pieces of the…
Splitting and projection-type algorithms have been applied to many optimization problems due to their simplicity and efficiency, but the application of these algorithms to optimal control is less common. In this paper we utilize the…
In this paper we present the successive centralization of the circumcenter reflection scheme with several control sequences for solving the convex feasibility problem in Euclidean space. Assuming that a standard error bound holds, we prove…