On consistency of bounding operations in deterministic global optimization (Q1101343)

This technical comment refers to the discussion of strong consistency of several bounding procedures in Lemma 2.1 and Proposition 2.1 of a previous paper of the author [ibid. 58, 11-27 (1988; Zbl 0621.90064)]. A necessary clarification is given of the notion of convergence \(\phi _ q\to \phi\) in Lemma 2.1, and a derivation of Proposition 2.1 is presented that includes a new and simple consistency proof of the classical bounding by convex envelopes used in many branch-and-bound procedures.