ﻻ يوجد ملخص باللغة العربية
This paper proposes TriPD, a new primal-dual algorithm for minimizing the sum of a Lipschitz-differentiable convex function and two possibly nonsmooth convex functions, one of which is composed with a linear mapping. We devise a randomized block-coordinate version of the algorithm which converges under the same stepsize conditions as the full algorithm. It is shown that both the original as well as the block-coordinate scheme feature linear convergence rate when the functions involved are either piecewise linear-quadratic, or when they satisfy a certain quadratic growth condition (which is weaker than strong convexity). Moreover, we apply the developed algorithms to the problem of multi-agent optimization on a graph, thus obtaining novel synchronous and asynchronous distributed methods. The proposed algorithms are fully distributed in the sense that the updates and the stepsizes of each agent only depend on local information. In fact, no prior global coordination is required. Finally, we showcase an application of our algorithm in distributed formation control.
This paper investigates accelerating the convergence of distributed optimization algorithms on non-convex problems. We propose a distributed primal-dual stochastic gradient descent~(SGD) equipped with powerball method to accelerate. We show that the
We consider a distributed optimization problem over a network of agents aiming to minimize a global objective function that is the sum of local convex and composite cost functions. To this end, we propose a distributed Chebyshev-accelerated primal-du
This paper studies the distributed optimization problem where the objective functions might be nondifferentiable and subject to heterogeneous set constraints. Unlike existing subgradient methods, we focus on the case when the exact subgradients of th
This work studies multi-agent sharing optimization problems with the objective function being the sum of smooth local functions plus a convex (possibly non-smooth) function coupling all agents. This scenario arises in many machine learning and engine
We consider the zeroth-order optimization problem in the huge-scale setting, where the dimension of the problem is so large that performing even basic vector operations on the decision variables is infeasible. In this paper, we propose a novel algori