The development of nonlinear optimization algorithms capable of performing reliably in the presence of noise has garnered considerable attention lately. This paper advocates for strategies to create noise-tolerant nonlinear optimization algorithms by adapting classical deterministic methods. These adaptations follow certain design guidelines described here, which make use of estimates of the noise level in the problem. The application of our methodology is illustrated by the development of a line search gradient projection method, which is tested on an engineering design problem. It is shown that a new self-calibrated line search and noise-aware finite-difference techniques are effective even in the high noise regime. Numerical experiments investigate the resiliency of key algorithmic components. A convergence analysis of the line search gradient projection method establishes convergence to a neighborhood of stationarity.

翻译：近年来，开发能够在噪声环境下可靠运行的非线性优化算法受到了广泛关注。本文提出通过改进经典确定性方法来构建噪声容忍非线性优化算法的策略。这些改进遵循本文所述的设计准则，其核心在于利用问题中噪声水平的估计信息。我们通过开发线搜索梯度投影法来展示该方法的应用，并在工程设计问题上进行测试。研究表明，新型自校准线搜索技术与噪声感知有限差分方法即使在高噪声环境下依然有效。数值实验考察了关键算法组件的鲁棒性。对线搜索梯度投影法的收敛性分析证明了算法能够收敛至平稳点的邻域内。