N-Dimension Golden Section Search: Its Variants and Limitations

One-dimension (1-D) golden section search (GSS) is widely used in many fields. This algorithm is very suitable for searching without derivative for the extrema of objective functions with unimodal. Two-dimension (2-D) GSS was also implemented and used for object tracking. In this paper, a structured n-dimension GSS and its variants are proposed. It has been shown that 1-D GSS is the fastest algorithm except for Fibonacci search. However, the efficiency of n-dimension GSS, n > 1, is generally not the case. The phenomenon will be analyzed and experimented. In addition, the limitations of n-D GSS are also illustrated. These concepts are very important for the future use of GSS.