Backtracking Line Search and the Armijo Condition

Here is the bowl from the gradient descent section: one half of x one squared plus five halves of x two squared. Its largest curvature is five, so a fixed step converges only below two over five.

Take a step a little too large. Along the steep direction the factor is now below minus one, so each step flips the sign and grows: the red path climbs out of the valley.

The rest of the narration is in the book's Companion.