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 the solution.

翻译：近年来，能够在噪声环境下稳定运行的非线性优化算法开发备受关注。本文提出通过改进经典确定性方法构建噪声容忍非线性优化算法的策略。改进方案遵循本文所述的设计准则，利用问题的噪声水平估计值。我们以线搜索梯度投影法的开发为例展示该方法的应用，并在工程设计问题中进行了测试。研究表明，新型自校准线搜索和噪声感知有限差分技术即使在强噪声环境下依然有效。数值实验探究了关键算法组件的鲁棒性。线搜索梯度投影法的收敛性分析证明其能收敛至解的邻域。