{
  "id": "2303.16659",
  "version": "v1",
  "published": "2023-03-29T13:07:50.000Z",
  "updated": "2023-03-29T13:07:50.000Z",
  "title": "Safe Zeroth-Order Optimization Using Quadratic Local Approximations",
  "authors": [
    "Baiwei Guo",
    "Yuning Jiang",
    "Giancarlo Ferrari-Trecate",
    "Maryam Kamgarpour"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2211.02645",
  "categories": [
    "math.OC",
    "cs.SY",
    "eess.SY"
  ],
  "abstract": "This paper addresses black-box smooth optimization problems, where the objective and constraint functions are not explicitly known but can be queried. The main goal of this work is to generate a sequence of feasible points converging towards a KKT primal-dual pair. Assuming to have prior knowledge on the smoothness of the unknown objective and constraints, we propose a novel zeroth-order method that iteratively computes quadratic approximations of the constraint functions, constructs local feasible sets and optimizes over them. Under some mild assumptions, we prove that this method returns an $\\eta$-KKT pair (a property reflecting how close a primal-dual pair is to the exact KKT condition) within $O({1}/{\\eta^{2}})$ iterations. Moreover, we numerically show that our method can achieve faster convergence compared with some state-of-the-art zeroth-order approaches. The effectiveness of the proposed approach is also illustrated by applying it to nonconvex optimization problems in optimal control and power system operation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-29T13:07:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quadratic local approximations",
      "safe zeroth-order optimization",
      "addresses black-box smooth optimization problems",
      "paper addresses black-box smooth optimization",
      "primal-dual pair"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}