Class 5

Line Search Methods (Chapter 3),
of type
x_{k+1}= x_{k}+ alpha_{k} p_{k},
where p_{k} is the search direction and
alpha_{k} is the step length

Step Length

Wolfe conditions (geometric interpretations)
sufficient decrease  step is not too large
curvature condition  step is not too small

Lemma 3.1 (existence of step lengths)

Convergence of Line Search Methods

Theorem 3.2 (cos theta geometric interpretation)