Multisection in interval branch-and-bound methods for global optimization - I. Theoretical results

We have investigated variants of interval branch-and-bound algorithms for g lobal optimization where the bisection step was substituted by the subdivis ion of the current, actual interval into many subintervals in a single iter ation step. The convergence properties of the multisplitting methods, an im portant class of multisection procedures are investigated in detail. We als o studied theoretically the convergence improvements caused by multisection on algorithms which involve the accelerating tests (like e.g. the monotoni city test). The results are published in two papers, the second one contain s the numerical test result.