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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)

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 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 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)

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)

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)

- T Csendes, And D Ratz, Siam J Anal Numer
- 1997

The role of the interval subdivision selection rule is investigated in branch-and-bound algorithms for global optimization. The class of rules that allow convergence for the model algorithm is characterized, and it is shown that the four rules investigated satisfy the conditions of convergence. A numerical study with a wide spectrum of test problems… (More)

The paper presents a new verified optimization method for the problem of finding the densest packings of non-overlapping equal circles in a square. In order to provide reliable numerical results, the developed algorithm is based on interval analysis. As one of the most efficient parts of the algorithm, an interval-based version of a previous elimination… (More)

The present review paper summarizes the research work done mostly by the authors on packing equal circles in the unit square in the last years. The problem of finding the densest packing of n equal objects in a bounded space is a classical one which arises in many scientific and engineering fields. For the two-dimensional case, it is a well-known problem of… (More)