<p>A trust region gradient sampling algorithm that is applicable for solving nonsmooth unconstrained optimization problems in noisy environments is proposed, where a noisy environment is a scenario in which the function evaluation and gradient evaluation cannot be obtained precisely. The new algorithm constitutes a generalization of the basic trust region method. In the new approach, the subgradient used to formulate the trust region subproblem is computed through the gradient sampling approach. A novel reduction test is proposed to control the impact of noise on the performance of the developed algorithm. Under reasonable assumptions, the iterations of the algorithm ultimately enter one neighborhood and infinitely visit another neighborhood encompassed therein. The structures of these two neighborhoods are presented in this paper. Finally, the validity of the new algorithm is verified through numerical experiments.</p>

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A trust region gradient sampling method for noisy nonsmooth convex optimization

  • Tianyou Shang,
  • Ke Su

摘要

A trust region gradient sampling algorithm that is applicable for solving nonsmooth unconstrained optimization problems in noisy environments is proposed, where a noisy environment is a scenario in which the function evaluation and gradient evaluation cannot be obtained precisely. The new algorithm constitutes a generalization of the basic trust region method. In the new approach, the subgradient used to formulate the trust region subproblem is computed through the gradient sampling approach. A novel reduction test is proposed to control the impact of noise on the performance of the developed algorithm. Under reasonable assumptions, the iterations of the algorithm ultimately enter one neighborhood and infinitely visit another neighborhood encompassed therein. The structures of these two neighborhoods are presented in this paper. Finally, the validity of the new algorithm is verified through numerical experiments.