{
  "id": "1810.10439",
  "version": "v1",
  "published": "2018-10-24T15:09:11.000Z",
  "updated": "2018-10-24T15:09:11.000Z",
  "title": "A recursively feasible and convergent Sequential Convex Programming procedure to solve non-convex problems with linear equality constraints",
  "authors": [
    "Josep Virgili-Llop",
    "Marcello Romano"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "A computationally efficient method to solve non-convex programming problems with linear equality constraints is presented. The proposed method is based on a recursively feasible and descending sequential convex programming procedure proven to converge to a locally optimal solution. Assuming that the first convex problem in the sequence is feasible, these properties are obtained by convexifying the non-convex cost and inequality constraints with inner-convex approximations. Additionally, a computationally efficient method is introduced to obtain inner-convex approximations based on Taylor series expansions. These Taylor-based inner-convex approximations provide the overall algorithm with a quadratic rate of convergence. The proposed method is capable of solving problems of practical interest in real-time. This is illustrated with a numerical simulation of an aerial vehicle trajectory optimization problem on commercial-of-the-shelf embedded computers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-24T15:09:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convergent sequential convex programming procedure",
      "linear equality constraints",
      "non-convex problems",
      "vehicle trajectory optimization problem",
      "recursively feasible"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}