{
  "id": "2006.14921",
  "version": "v1",
  "published": "2020-06-26T11:49:57.000Z",
  "updated": "2020-06-26T11:49:57.000Z",
  "title": "Scalable Method for Linear Optimization of Industrial Processes",
  "authors": [
    "Leonid B. Sokolinsky",
    "Irina M. Sokolinskaya"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "In the development of industrial digital twins, the optimization problem of technological and business processes often arises. In many cases, this problem can be reduced to a large-scale linear programming (LP) problem. The article is devoted to the new method for solving large-scale LP problems. This method is called the \"apex-method\". The apex-method uses the predictor-corrector framework. The predictor step calculates a point belonging to the feasible region of LP problem. The corrector step calculates a sequence of points converging to the exact solution of the LP problem. The article gives a formal description of the apex-method and provides information about its parallel implementation in C++ language by using the MPI library. The results of large-scale computational experiments on a cluster computing system to study the scalability of the apex method are presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-26T11:49:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "linear optimization",
      "industrial processes",
      "scalable method",
      "solving large-scale lp problems",
      "apex-method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}