In this interesting paper, the authors discuss the important problem of determining the minimum value of a convex function. In the introduction, they give an overview of standard algorithms for this task and describe their salient properties. Next, they present the class of algorithms to be analyzed and prove several theorems, including a global convergence result. No numerical illustrations are given.

This is a technical paper for specialists. The presentation is clear and well organized. The list of references is adequate and contains 20 items.