UNCONSTRAINED MINIMIZATION BY COMBINING THE DYNAMIC AND CONJUGATE GRADIENT METHODS

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Abstract
The author has recently developed a gradient-only dynamic method for unconstrained minimization. The main drawback of this method is, that in spite of rapid motion towards the neighbourhood of a local minimum, the final convergence is slow. To improve the situation the possibility of switching from the dynamic method to a conjugate qradient type method near the minimum is investigated. The Fletcher-Reeves conjugate gradient method is applied in a way in which only gradient evaluations are used by exploiting an Euler—trapezium integration scheme. The numerical results obtained are promising, indicating the combined method to be competitive for problems of high dimensionality and where the gradient evaluations are re1atively inexpensive.
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