Steepest descent method and how to find the weighting factor

Question

I am trying to understand the numerical method of finding a minimum, the steepest descent method. \begin{equation} x_1 = x_0 - \alpha \frac{df}{dx} \end{equation} I understand the idea behind it and how to set up the equation, but I do not get:

• How to find the "right" weighting factor $\alpha$.

• Why the next search has to occur orthogonal to the previous search direction.

Thanks in advance for the answers.

Answer 1

For the second part, you can see the book "Nonlinear Programming:Theory and Algorithms",written by Mokhtar S.Bazaraa and H.D.Sherali. 3rd edtion. Page389. It is zigzagging .