An Evaluation and Comparison of Several Single Variable Search Methods
NAVAL POSTGRADUATE SCHOOL MONTEREY CA
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This study compares three single variable search methods - Golden Section, cubic interpolation and quadratic interpolation. The SUMT nonlinear program was used for the comparison. The OPT subroutine which performs the single variable search in SUMT currently uses the Golden Section method. Two different OPT subroutines were written which implemented cubic interpolation and quadratic interpolation. Seven test problems which contained 9-100 variables and 2-20 constraints were used. The comparison was made on computation time per single variable search for the three methods and the number of function evaluations per single variable search for the Golden Section and quadratic interpolation methods. A single variable search by Lasdon, Fox and Ratner and one by Fletcher and McCann were also discussed. The results showed that the quadratic interpolation was slightly faster than the other two methods and required fewer function evaluations per single variable search than the Golden Section method.
- Operations Research