Quoting: "We introduce a new energy function and a corresponding new update rule which is guaranteed to converge to a local minimum of the energy function." Is

Quoting: "We introduce a new energy function and a corresponding new update rule which is guaranteed to converge to a local minimum of the energy function." Is this a minimum in a local area or local in the range of some function? I could see perhaps that'd being an advantage if you happen to know that local part of the range In contrast we're usually looking for global min/max say with annealing algorithms. How is local is better in the context of this paper than global?