  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.
