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<p>In this paper, we study the empirical residual optimization problem with a least squares loss function. A stochastic variance reduced Levenberg–Marquardt method is proposed for solving it. It is shown that both the estimates and the models of the objective function are probabilistically weak accurate if the sample size is chosen appropriately. Moreover, the method converges to a stationary point of the problem almost surely under certain conditions.</p>

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Convergence of a stochastic variance reduced Levenberg–Marquardt method

  • 期刊论文

  • 发表日期：

    2025年1月3日

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  • Weiyi Shao,
  • Jinyan Fan

摘要

In this paper, we study the empirical residual optimization problem with a least squares loss function. A stochastic variance reduced Levenberg–Marquardt method is proposed for solving it. It is shown that both the estimates and the models of the objective function are probabilistically weak accurate if the sample size is chosen appropriately. Moreover, the method converges to a stationary point of the problem almost surely under certain conditions.