An efficient quadratic fit—Sectioning algorithm for minimization without derivatives Original Research Article

This paper presents a new quadratic fit golden section algorithm for finding the minimum of a one variable function without using derivatives. The algorithm starts with the establishment of an initial bracket defining a three point pattern, with the function value at the middle point being the least value of the three. A quadratic fit is applied to the three point pattern and is considered for acceptance when it is close to the quadratic minimum at the previous iteration. Some properties of the location of the quadratic minimum point are established and the criteria for acceptance are developed. Golden sectioning of the larger interval is done when quadratic minimum is not accepted. The results of the new algorithm compare well with the established hybrid procedures.