Related papers: Distributed MIN-MAX Optimization Application to Ti…
Random projection algorithm is an iterative gradient method with random projections. Such an algorithm is of interest for constrained optimization when the constraint set is not known in advance or the projection operation on the whole…
Minimax optimization problems are an important class of optimization problems arising from modern machine learning and traditional research areas. While there have been many numerical algorithms for solving smooth convex-concave minimax…
This paper considers a distributed convex optimization problem with inequality constraints over time-varying unbalanced digraphs, where the cost function is a sum of local objectives, and each node of the graph only knows its local…
This article reports an algorithm for multi-agent distributed optimization problems with a common decision variable, local linear equality and inequality constraints and set constraints with convergence rate guarantees.…
This paper focuses on a class of inclusion problems of maximal monotone operators in a multi-agent network, where each agent is characterized by an operator that is not available to any other agents, but the agents can cooperate by…
A popular method for finding the projection onto the intersection of two closed convex subsets in Hilbert space is Dykstra's algorithm. In this paper, we provide sufficient conditions for Dykstra's algorithm to converge rapidly, in finitely…
In this paper, we consider a class of nonconvex problems with linear constraints appearing frequently in the area of image processing. We solve this problem by the penalty method and propose the iteratively reweighted alternating…
We present distributed subgradient methods for min-max problems with agreement constraints on a subset of the arguments of both the convex and concave parts. Applications include constrained minimization problems where each constraint is a…
This article describes a set of methods for quickly computing the solution to the regularized optimal transport problem. It generalizes and improves upon the widely-used iterative Bregman projections algorithm (or Sinkhorn--Knopp…
The paper studies a distributed constrained optimization problem, where multiple agents connected in a network collectively minimize the sum of individual objective functions subject to a global constraint being an intersection of the local…
In 1933 von Neumann proved a beautiful result that one can approximate a point in the intersection of two convex sets by alternating projections, i.e., successively projecting on one set and then the other. This algorithm assumes that one…
This article details a general numerical framework to approximate so-lutions to linear programs related to optimal transport. The general idea is to introduce an entropic regularization of the initial linear program. This regularized…
This paper studies distributed algorithms for the extended monotropic optimization problem, which is a general convex optimization problem with a certain separable structure. The considered objective function is the sum of local convex…
Feasibility problem aims to find a common point of two or more closed (convex) sets whose intersection is nonempty. In the literature, projection based algorithms are widely adopted to solve the problem, such as the method of alternating…
We apply the Min-Sum message-passing protocol to solve the consensus problem in distributed optimization. We show that while the ordinary Min-Sum algorithm does not converge, a modified version of it known as Splitting yields convergence to…
The averaged alternating modified reflections (AAMR) method is a projection algorithm for finding the closest point in the intersection of convex sets to any arbitrary point in a Hilbert space. This method can be seen as an adequate…
In this paper, we formulate and solve a randomized optimal consensus problem for multi-agent systems with stochastically time-varying interconnection topology. The considered multi-agent system with a simple randomized iterating rule…
We study the alternating algorithm for the computation of the metric projection onto the closed sum of two closed subspaces in uniformly convex and uniformly smooth Banach spaces. For Banach spaces which are convex and smooth of power type,…
This paper addresses constrained smooth saddle-point problems in settings where projection onto the feasible sets is computationally expensive. We bridge the gap between projection-based and projection-free optimization by introducing a…
A multi-agent optimization problem motivated by the management of energy systems is discussed. The associated cost function is separable and convex although not necessarily strongly convex and there exist edge-based coupling equality…