LINE SEARCH ALGORITHMS WITH GUARANTEED SUFFICIENT DECREASE

The development of software for minimization problems is often based on a line search method. We consider line search methods that satisfy sufficient decrease and curvature conditions, and formulate the problem of determining a point that satisfies these two conditions in terms of finding a point in a set T(mu). We describe a search algorithm for this problem that produces a sequence of iterates that converge to a point 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 terminates within a small number of iterations.