Investigation on Scaled CG-Type Algorithms for Unconstrained Optimization

In this paper, we describe two new algorithms which are modifications of the Hestens-stiefl CG-method. The first is the scaled CG-method (obtained from function and gradient-values) which improves the search direction by multiplying to a scalar obtained from function value and its gradient at two successive points along the iterations. The second is the Preconditioned CG-method which uses an approximation at Hessein of the minimizing function. These algorithms are not sensitive to the line searches. Numerical experiments indicate that these new algorithms are effective and superior especially for increasing dimensionalities.