A new unidimensional search method for optimization: Linear interpolation method

This paper presents a new unidimensional search method for non-linear and unconstrained optimization based on finding an intersection point of the lines which pass the extreme points of the interval of uncertainty, [a(k),b(k)], and their neighbor points of the function. If f(x) is strictly convex function, the lines intersect at a point between a(k) and b(k). The iteration formula is derived by solving the linear equation. The performance of the new method, named the linear interpolation method, is analyzed in terms of the most popular and widely used criteria; the number of iterations, the number of function evaluations, and the computer (CPU) time in comparison with the most effectual methods such as the Quadratic Interpolation, Golden Section, RMS, and AM methods, using 10 test functions. (c) 2005 Elsevier Inc. All rights reserved.