On the convergence of adaptive partition algorithms in global optimization

Abstract

In [8] a broad class of adaptive partition algorithms was introduced for finding the global minimize r(s) of a multiextremal Lipschitz-continuous function defined on an ndimensional interval feasible region. In [20], Zilinskas claims that the general convergence result (Theorem 2.1) of [8] is not correct, providing a (false) counterexample. Besides showing the fallacy of his argumentation, some additional points on the subject of convergent partition strategies are also summarized.