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This paper investigates the innuence of the interval subdivision selection rule on the convergenceof interval branch-and-bound algorithmsfor global optimization. For the class of rules that allows convergence, we study the eeects of the rules on a model algorithm with special list ordering. Four diierent rules are investigated in theory and in practice. A(More)
In this two-part article, nonlinear coordinate transformations are discussed to simplify unconstrained global optimization problems and to test their unimodality on the basis of the analytical structure of the objective functions. If the transformed problems are quadratic in some or all the variables, then the optimum can be calculated directly, without an(More)
We have investigated variants of interval branch-and-bound algorithms for global optimization where the bisection step was substituted by the subdivision of the current, actual interval into many subintervals in a single iteration step. The convergence properties of the multisplitting methods, an important class of multisection procedures are investigated(More)
We have investigated variants of interval branch-and-bound algorithms for global optimization where the bisection step was substituted by the subdivision of the current, actual interval into many subintervals in a single iteration step. The results are published in two papers, the first one contains the theoretical investigations on the convergence(More)
We present a new verified optimization method to find regions for Hénon systems where the conditions of chaotic behaviour hold. The present paper provides a methodology to verify chaos for certain mappings and regions. We discuss first how to check the set theoretical conditions of a respective theorem in a reliable way by computer programs. Then we(More)
The present paper is devoted to studying Hubbard's pendulum equation ¨ x + 10 −1 ˙ x + sin(x) = cos(t). By rigorous/interval methods of computation, the main assertion of Hubbard on chaos properties of the induced dynamics is lifted from the level of experimentally observed facts to the level of a theorem completely proved. A distinguished family of(More)
We describe a new implementation of an interval optimization algorithm with focus on the software related issues. The algorithm implemented in MATLAB that uses the INTLAB package supporting interval calculations and automatic differentiation solves the bound constrained global optimization problem. The method itself is a simplified version of those interval(More)