{
  "id": "1510.08580",
  "version": "v1",
  "published": "2015-10-29T07:07:40.000Z",
  "updated": "2015-10-29T07:07:40.000Z",
  "title": "Primal-Dual Algorithm for Distributed Constrained Optimization",
  "authors": [
    "Jinlong Lei",
    "Han-Fu Chen",
    "Hai-Tao Fang"
  ],
  "comment": "8 pages, 3 figures",
  "categories": [
    "math.OC"
  ],
  "abstract": "This paper studies the distributed 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 constraint sets assigned to the agents. Based on the augmented Lagrange technique, a primal-dual algorithm with a projection operation included is proposed to solve the problem. It is found that with appropriately chosen constant step-size, the estimates derived at all agents finally reach the consensus: they all tend to the optimal solution. In addition, the value of the cost function at the time-averaged estimate converges to the optimal value at the rate $O(\\frac{1}{k})$ for the case where there is no constraint. By these properties the proposed primal-dual algorithm is distinguished from the existing algorithms for the deterministic constrained optimization. The theoretical analysis is justified by the numerical simulation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-29T07:07:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "primal-dual algorithm",
      "distributed constrained optimization",
      "local constraint sets",
      "individual objective functions subject",
      "projection operation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}