New and efficient unidimensional search schemes for optimization

This paper describes three new unidimensional search schemes namely the Arithmetic Mean method, the Geometric Mean method and the Harmonic Mean method. Though all the three methods have the most desirable feature of robustness, the Arithmetic Mean and Harmonic Mean methods are found to be faster in convergence. Numerical experiments conducted on typical unidimensional test functions establish the superiority of the Arithmetic Mean and Harmonic Mean methods over the existing RMS, Cubic Interpolation, Quadratic Interpolation and Golden Section methods, in terms of number of function evaluations and CPU-time. Approximate versions of these methods are also defined.