{
  "id": "1402.7291",
  "version": "v3",
  "published": "2014-02-28T16:01:49.000Z",
  "updated": "2014-05-27T07:40:26.000Z",
  "title": "Optimal subgradient algorithms with application to large-scale linear inverse problems",
  "authors": [
    "Masoud Ahookhosh"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "This study addresses some algorithms for solving structured unconstrained convex optimiza- tion problems using first-order information where the underlying function includes high-dimensional data. The primary aim is to develop an implementable algorithmic framework for solving problems with multi- term composite objective functions involving linear mappings using the optimal subgradient algorithm, OSGA, proposed by Neumaier in [49]. To this end, we propose some prox-functions for which the cor- responding subproblem of OSGA is solved in a closed form. Considering various inverse problems arising in signal and image processing, machine learning, statistics, we report extensive numerical and compar- isons with several state-of-the-art solvers proposing favourably performance of our algorithm. We also compare with the most widely used optimal first-order methods for some smooth and nonsmooth con- vex problems. Surprisingly, when some Nesterov-type optimal methods originally proposed for smooth problems are adapted for solving nonsmooth problems by simply passing a subgradient instead of the gradient, the results of these subgradient-based algorithms are competitive and totally interesting for solving nonsmooth problems. Finally, the OSGA software package is available.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-05-27T07:40:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90C25",
      "90C60",
      "49M37",
      "65K05"
    ],
    "keywords": [
      "large-scale linear inverse problems",
      "optimal subgradient algorithm",
      "solvers proposing favourably performance",
      "solving nonsmooth problems",
      "application"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.7291A"
    }
  }
}