{
  "id": "1611.09260",
  "version": "v1",
  "published": "2016-11-28T17:50:41.000Z",
  "updated": "2016-11-28T17:50:41.000Z",
  "title": "The LP-Newton Method and Conic Optimization",
  "authors": [
    "Francesco Silvestri",
    "Gerhard Reinelt"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "We propose that the LP-Newton method can be used to solve conic LPs over a 'conic interval', whenever linear optimization over an unconstrained conic interval is easy. In particular, if $\\leq_\\mathcal{K}$ is the partial order induced by a proper convex cone $\\mathcal{K}$, then conic LPs over $[l,u]_{\\mathcal{K}}=\\{ l\\leq_\\mathcal{K} x\\leq_\\mathcal{K} u\\}$ can be solved whenever optimizing a linear function over $[l,u]_{\\mathcal{K}}$ is fast. This generalizes the result for the case of $\\mathcal{K}=\\mathbb{R}^n_+$ that was originally proposed for using the method. Specifically, we show how to adapt this method for both SOCP and SDP problems and illustrate the method with a few experiments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-28T17:50:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90C05",
      "90C53",
      "90C22"
    ],
    "keywords": [
      "lp-newton method",
      "conic optimization",
      "conic lps",
      "proper convex cone",
      "linear optimization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}