Finite exact branch-and-bound algorithms for concave minimization over polytopes

In this paper simplicial branch-and-bound algorithms for concave minimization problems are discussed. Some modifications of the basic algorithm are presented, mainly consisting in rules to start local searches, introduction of cuts and updates of the original objective function. While some of these tools are not new in the literature, it is the first time, to the authors' knowledge, that they are used to guarantee the finiteness of a simplicial branch-and-bound approach.