Unconstrainted problem -- set descent direction and step length


Consider the following surface z = f(x,y) (viewed from two different angles):


The minimum is achieved at the black dot:


Given an initial guess, as shown by the black dot in the following graph:


Let us select a descent direction, which is shown as the arrow in the following graph:

(A descent direction is a direction such that the directional derivative of f(x,y) on this direction is less than 0.)


Next, following the chosen direction, we project the path on the furface z=f(x,y). This is show by the red curve in the following graph:


Build a coordinate system as following, and view the 2-D curve in this coordinate system: