Abstract: The paper highlights a failure in the implementation of a recommendation for the modified Newton’s method using a Rosenbrock type of functions that have slow convergence with two minimum points as test functions. The study finds that a recommended procedure, if the Hessian  at a point is not positive definite, may not lead to the desired optimal solution particularly when the initial point is not close enough to the expected solution. It has been demonstrated how to go round this problem. The results show that more than one technique may be required to determine all critical points of a given function.

Optimization, Rosenbrock’s function, Modified Newton’s Method, Descent direction

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