A derivative-based bracketing scheme for univariate minimization and the conjugate gradient method (Q1825603)

The author develops a derivative-based univariate minimization algorithm which combines a bracketing strategy, the bisection method and Hermite cubic interpolation. It is proved that the proposed algorithm achieves quadratic convergence using one function and one derivative evaluation each iteration. Also the author proposes an efficient conjugate gradient search scheme which incorporate the derivative-based univariate algorithm. Some experimental results are presented.