A NEW UNIDIMENSIONAL SEARCH METHOD FOR OPTIMIZATION

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Abstract
An endeavour is made in this paper to present a new and simple unidimensional search scheme for optimization. It has the most desirable features of robustness and fast convergence. Numerical experiments conducted on single dimension test functions clearly establish its superiority over presently existing unidimensional search schemes such as Cubic interpolation. Quadratic filling and Golden Section methods, (is effect on three quadratically convergent algorithms, the rank one algorithm (Algorithm I), the projection algorithm (Algorithm II) and the Fletcher-Reeves algorithm (Algorithm III) is also investigated in detail. In terms of the number of function evaluations and the CPU-time taken, its performance is found to be much better than the aforementioned schemes. Finally an approximate version of the scheme is defined whose performance is also thoroughly examined. It is found to take much less CPU-time with fewer function evaluations, without in any way impairing the accuracy of the final results.

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