Dynamic Ratio Golden Section Method for Single Variable Optimization Studies

Golden section is a proven, robust and high utility single variable optimization method of use in many engineering disciplines. In its typical implementation, a fixed ratio (also known as Golden ratio) is used to partition the left-right bracket in such a way that the two internal points are strategically placed to close-in on the minimum point. Practical usage of this fixed ratio method shows good performance in progressive movement of x2 internal point to the minimum value. However, the fixed ratio method could not capture or follow the curve of rapidly changing function well. Herein, an improved Golden section method with dynamic ratio for partitioning the bracket is formulated and tested on a demonstrative case to optimize a quadratic function. Due to lack of computational power on a GPU budget laptop, more tests could not be conducted on this dynamic ratio Golden section method. Initial results obtained showed that the dynamic ratio does place the x2 internal point closer to the right bracket in regions of rapidly changing value. Overall, the dynamic ratio Golden section method reached convergence to the minimum point in 3 iterations compared to 12 iterations for the conventional fixed ratio Golden section method in a demonstrative case.