Golden Section Search Method for One-Dimensional Optimization

This section introduces a highly practical and straightforward search technique known as the Golden Section Search method. The Golden Section Search is an efficient one-dimensional optimization algorithm designed to rapidly locate optimal solutions within a defined interval. Its simplicity makes it accessible to users across various technical backgrounds. The algorithm operates on the principle of the golden ratio (approximately 1.618), recursively partitioning the search space according to this proportion to progressively narrow down the optimal region. Key implementation steps include initial boundary definition, iterative interval reduction using golden ratio proportions, and convergence criteria checking. From a coding perspective, the method typically requires less than 20 lines of implementation in languages like Python or MATLAB, involving basic arithmetic operations and conditional checks. By employing this method, users can significantly reduce computational time while improving search precision, making it particularly valuable for optimizing unimodal functions. We strongly recommend adopting this robust and computationally efficient search technique for one-dimensional optimization problems.