An efficient and derivative-free algorithm for finding the minimum of a 1-D user-defined function
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An efficient algorithm was developed for finding the minimum or maximum of a one-dimensional (1-D) user-defined function. The algorithm combined the quadratic interpolation, the Golden search, and an additional side search into a unified optimal search. Five 1-D, four 2-D, and two 4-D functions were used to test the proposed search method and compare it with the Golden search and the Brent 1-D algorithm, for various initial points or intervals. The test results showed that the proposed search method was significantly faster than Brent's search and the Golden search. The proposed search method did not experience any possible pre-termination problems either due to machine precision limit or a possible failure of interpolation. Brent's search method, however, was found to yield a wrong solution (pre-termination) for one of the test functions. 1993.
