{
  "id": "1607.01655",
  "version": "v1",
  "published": "2016-07-06T15:03:32.000Z",
  "updated": "2016-07-06T15:03:32.000Z",
  "title": "L1 penalization of volumetric dose objectives in optimal control of PDEs",
  "authors": [
    "Richard C. Barnard",
    "Christian Clason"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "This work is concerned with a class of optimal control problems governed by a partial differential equation that are motivated by an application in radiotherapy treatment planning, where the primary design objective is to minimize the volume where a functional of the state violates a prescribed level, but prescribing these levels in the form of pointwise state constraints can lead to infeasible problems. We therefore propose an alternative approach based on $L^1$ penalization of the violation. We establish well-posedness of the corresponding optimal control problem, derive first-order optimality conditions, and present a semismooth Newton method for the efficient numerical solution of these problems. The performance of this method for a model problem is illustrated and contrasted with the alternative approach based on (regularized) state constraints.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-06T15:03:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "volumetric dose objectives",
      "l1 penalization",
      "state constraints",
      "derive first-order optimality conditions",
      "corresponding optimal control problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}