Theoretical Convergence Analysis of a General Division–deletion Algorithm for Solving Global Search Problems

Presented in this paper is the prototype of a very general algorithm referred to as Division – Deletion Algorithm (DDA) for solving the most general global search problem. Various necessary conditions, sufficient conditions, and necessary and sufficient conditions for the convergence of the algorithm are proposed and analyzed. As an example of its application, we demonstrate that the convergence of a standard Hansen’s interval algorithm for unconstrained global optimization simply follows from this general theory.