On the global stabilization of locally convergent algorithms

There are a number of algorithms in the literature which both theoretically and empirically are known to be only locally convergent. These include such well known algorithms as secant, Newton, quasi-Newton and primal-dual algorithms. Locally, these algorithms tend to be highly efficient. Consequently, it is very desirable to find ways of extending, or modifying, these algorithms, so that they become globally convergent while retaining their attractive local properties. This paper describes a set of techniques which have recently emerged for stabilizing such algorithms and illustrates their application by means of a number of examples.