Distributed Convex Optimization Algorithms Based On Multi-Agent Systems

Recently,distributed convex optimization using multi-agent system has received much attention by many researchers.This problem is frequently approached by combining the consensus algorithms in multi-agent literature and the gradient algorithms in convex optimization literature.Existing,distributed algorithms for constrained optimization problems involve projection nonlinearity and thus difficult to analyze.To avoid gradient projection,this paper presents a novel distributed convex optimization algorithm in continuous-time by using mirror design.The resulting optimization dynamics it is designed in a primal-dual framework,where the primal and dual dynamics are respectively designed by the mirror descent and mirror ascent.The main contribution of this paper are as follows:1.The continuous-time mirror algorithms are illustrated in this paper,and a general method of proving convergence is given.The algorithms in this paper complement discrete-time mirror algorithms in existing literature.2.The multi-agent system theory is applied to the continuous-time mirror algorithm design,Which gives rise to a general framework of distributed convex optimization based on mirror design.3.The continuous-time mirror algorithms are utilized to deal with distributed convex optimization with constraints.This treatment mirror design has the advantage of avoiding gradient projection,and thus simplifies the computation and led aces the completely of the algorithms.