Line search is a fundamental part of iterative optimization methods for unconstrained and bound-constrained optimization problems to determine suitable step lengths that provide sufficient improvement in each iteration. Traditional line search methods are based on iterative interval refinement, where valuable information about function value and gradient is discarded in each iteration. We propose a line search method via Bayesian optimization, preserving and utilizing otherwise discarded information to improve step-length choices. Our approach is guaranteed to converge and shows superior performance compared to state-of-the-art methods based on empirical tests on the challenging unconstrained and bound-constrained optimization problems from the CUTEst test set.

翻译：线搜索是无约束及边界约束优化问题中迭代优化方法的基本组成部分，用于确定能保证每次迭代获得充分改进的合适步长。传统线搜索方法基于迭代区间细化，在每次迭代中会丢弃函数值与梯度的宝贵信息。本文提出一种基于贝叶斯优化的线搜索方法，通过保留并利用原本会被丢弃的信息来改进步长选择。该方法具有收敛性保证，并在CUTEst测试集中具有挑战性的无约束及边界约束优化问题上，通过实证测试显示出优于现有先进方法的性能。