Multisection in interval branch-and-bound methods for global optimization. I: Theoretical results (Q1583690)

A global optimization problem is considered whose objective function \(f(\cdot)\) is defined over an \(n\)-dimensional box, and an inclusion function for \(f(\cdot)\) is known. Several interval branch-and-bound algorithms are proposed. The usual bisection step was substituted by the subdivision of the actual interval into many subintervals. The convergence properties are investigated theoretically as well as the convergence improvements by means of the acceleration tests. The numerical testing results are supposed to the published in a subsequent paper.