In numerical optimization, line-search and trust-region methods are two important classes of descent schemes, with well-understood global convergence properties. Here we consider ``accelerated'' versions of these methods, where the conventional iterate is allowed to be replaced by any point that produces at least as much decrease in the cost function as a fixed fraction of the decrease produced by the conventional iterate. A detailed convergence analysis reveals that global convergence properties of line-search and trust-region methods still hold when the methods are accelerated. The analysis is performed in the general context of optimization on manifolds, of which optimization in R^n is a particular case. This general convergence analysis sheds a new light on the behavior of several existing algorithms.
http://dx.doi.org/10.1137/08072019X : SIAM Journal on Numerical Analysis, Vol. 47, No. 2, pp. 997-1018, 2009