{
  "id": "2304.00435",
  "version": "v1",
  "published": "2023-04-02T02:54:41.000Z",
  "updated": "2023-04-02T02:54:41.000Z",
  "title": "On Degeneracy Issues in Multi-parametric Programming and Critical Region Exploration based Distributed Optimization",
  "authors": [
    "Haitian Liu",
    "Ye Guo",
    "Hao Liu",
    "Hongbin Sun"
  ],
  "categories": [
    "eess.SY",
    "cs.SY",
    "math.OC"
  ],
  "abstract": "This paper focuses on two aspects of interest related to multi-parametric linear/quadratic programming (mpLP/QP). First, we study degeneracy issues of mpLP/QP. A novel approach to deal with degeneracies is proposed to find all critical regions containing the given parameter. Our method leverages properties of the multi-parametric linear complementary problem, vertex searching technique, and complementary basis enumeration. Second, an improved critical region exploration (CRE) method to solve distributed LP/QP is proposed under a general mpLP/QP-based formulation. The improved CRE incorporates the proposed approach to handle degeneracies. A cutting plane update and an adaptive stepsize scheme are also integrated to accelerate convergence under different problem settings. The computational efficiency is verified on multi-area tie-line scheduling problems with various testing benchmarks and initial states.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-02T02:54:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "critical region exploration",
      "distributed optimization",
      "multi-parametric programming",
      "multi-parametric linear complementary problem",
      "method leverages properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}