Unconstrained optimization problems are typically solved using iterative methods, which often depend on line search techniques to determine optimal step lengths in each iteration. This paper introduces a novel line search approach. Traditional line search methods, aimed at determining optimal step lengths, often discard valuable data from the search process and focus on refining step length intervals. This paper proposes a more efficient method using Bayesian optimization, which utilizes all available data points, i.e., function values and gradients, to guide the search towards a potential global minimum. This new approach more effectively explores the search space, leading to better solution quality. It is also easy to implement and integrate into existing frameworks. Tested on the challenging CUTEst test set, it demonstrates superior performance compared to existing state-of-the-art methods, solving more problems to optimality with equivalent resource usage.

翻译：无约束优化问题通常采用迭代方法求解，此类方法往往依赖线搜索技术确定每次迭代中的最优步长。本文提出一种新颖的线搜索方法。传统的线搜索方法旨在确定最优步长，但常会舍弃搜索过程中的有价值数据，并专注于优化步长区间。本文提出一种基于贝叶斯优化的更高效方法，该方法利用所有可用数据点（即函数值和梯度），引导搜索向潜在全局最小值逼近。这种新方法能更有效地探索搜索空间，从而提升解的质量。该方法易于实现，并可集成到现有框架中。在具有挑战性的CUTEst测试集上进行测试表明，与现有最先进方法相比，该方法在同等资源消耗下能解决更多问题的优化问题，展现出优越性能。