A Regularized Saddle-Point Algorithm for （一个正规化的鞍点算法）.pdf

A Regularized Saddle-Point Algorithm for Networked Optimization with Resource Allocation Constraints — TECHNICAL REPORT — This is an extended version of a paper accepted for CDC 2012 with identical title Andrea Simonetto, Tam´as Keviczky, Mikael Johansson 2 1 0 Abstract— We propose a regularized saddle-point algorithm make use of regularization and solve the resulting strictly 2 for convex networked optimization problems with resource convex problem via a saddle-point method. Furthermore, we allocation constraints. Standard distributed gradient methods g incorporate the resource allocation equality constraints di- suffer from slow convergence and require excessive communi- u rectly into the saddle-point iterations by extending the results cation when applied to problems of this type. Our approach A offers an alternative way to address these problems, and ensures of [8] (originally proposed for unconstrained problems). We 6 that each iterative update step satisfies the resource allocation derive step-size conditions that guarantee convergence of our constraints. We derive step-size conditions under which the iterative scheme, and show how these results are linked to the ] distributed algorithm converges geometrically to the regularized problem characteristics and the graph topology, respectively. Y optimal value, and show how these conditions are affected by