Optimization of One-Dimensional Functions Using the Golden Section Search Method

Abstract

This paper addresses the problem of one-dimensional function optimization using the Golden Section Search Method. The primary objective is to determine the point at which a given unimodal function achieves its minimum within a bounded interval. The importance of such methods lies in their applicability to various scientific and engineering problems where analytical solutions may be complex or intractable. The study aims to explore both the theoretical background and practical implementation of the method, supported by an illustrative example. The research method involves analytical derivation of conditions for extrema, an explanation of unimodality, and step-by-step application of the Golden Section technique. The expected result is an accurate approximation of the function's minimum point with a specified level of precision, demonstrating the effectiveness and efficiency of the method in minimizing unimodal functions without requiring derivative information