Distributed Proximal Algorithms for Multiagent Optimization With Coupled Inequality Constraints

Abstract

This paper aims to address distributed optimization problems over directed, time-varying, and unbalanced networks, where the global objective function consists of a sum of locally accessible convex objective functions subject to a feasible set constraint and coupled inequality constraints whose information is only partially accessible to each agent. For this problem, a distributed proximal-based algorithm, called distributed proximal primal-dual (DPPD) algorithm, is proposed based on the celebrated centralized proximal point algorithm. It is shown that the proposed algorithm can lead to the global optimal solution with a general stepsize, which is diminishing and non-summable, but not necessarily square-summable, and the saddle-point running evaluation error vanishes proportionally to O(1/ √ k), where k > 0 is the iteration number. Finally, a simulation example is presented to corroborate the effectiveness of the proposed algorithm.

Distributed solver for linear matrix inequalities: an optimization perspective

“…Define a decision variable x i = [x i,1 , … , x i,m ] T ∈ ℝ m for each agent i, and the variable in a compact form over the network X = [x 1 , … , x n ] ∈ ℝ mn . Then problem (7) can be reformulated into where a ij is the (i, j)-th entry of the adjacency matrix of the multi-agent network. Note that the consensus constraint…”

“…In contrast to centralized methods, distributed algorithms aim to solve coupled problems, where each agent only has access to its local information and neighbors' decision variables. A number of distributed algorithms have been proposed, including mirror descent algorithms, the dual averaging methods and proximal algorithms [4][5][6][7].…”

Consensus of Heterogeneous Multi-Agent Systems Under Directed Topology

“…The theoretical frameworks of the consensus problem and the basic method of solving consensus were presented. Subsequently, second-order integrator agent systems [7], high-order integrator agent systems [8], nonlinear agent systems [9] and multi-agent systems in different application scenarios [10], [11] have been studied and some meaningful conclusions have been obtained. Inspired by the prominent work, the consensus problem in some special application scenarios was studied.…”

Distributed Primal-Dual Perturbation Algorithm Over Unbalanced Directed Networks

“…2) Compared with the existing primal-dual algorithms [12], [17], [22], the proposed primal-dual perturbation algorithm combines a fixed step-size rule for the computation of perturbation points and a diminishing step-size rule for the update of primal and dual variables. A numerical example illustrates that the proposed primal-dual perturbation algorithm converges faster than the gradient-based primal-dual algorithm.…”