Chapter 6: General Affordable Algorithms
Ernesto G. Birgin, José Mario Martínez · Society for Industrial and Applied Mathematics eBooks · 2014
In the global optimization literature, algorithms that are designed to converge not to global minimizers but to mere stationary points (in fact, not necessarily local minimizers) are known as local algorithms. This denomination could be adopted with a warning that local algorithms are generally guaranteed to converge in some sense to stationary points of the optimization problem, independently of the initial approximation. In this sense, they are said to be globally convergent. Roughly speaking, “local algorithm” is synonymous with the “affordable algorithm” of Chapter 3. In general, global optimization algorithms are not reliable for solving large-scale problems, and, for small to medium-scale problems, they are much slower than local algorithms. On the other hand, global optimization software makes use of local algorithms when associated with branch-and-bound procedures by means of which the search space for a global minimizer is reduced.