Jj. More et Dj. Thuente, LINE SEARCH ALGORITHMS WITH GUARANTEED SUFFICIENT DECREASE, ACM transactions on mathematical software, 20(3), 1994, pp. 286-307
The development of software for minimization problems is often based o
n a line search method. We consider line search methods that satisfy s
ufficient decrease and curvature conditions, and formulate the problem
of determining a point that satisfies these two conditions in terms o
f finding a point in a set T(mu). We describe a search algorithm for t
his problem that produces a sequence of iterates that converge to a po
int in T(mu) and that, except for pathological cases, terminates in a
finite number of steps. Numerical results for an implementation of the
search algorithm on a set of test functions show that the algorithm t
erminates within a small number of iterations.