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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 convergence properties of the multisplitting methods, an important class of multisection procedures are investigated… (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). Using rigorous/interval methods of computation, the main assertion of Hubbard on chaos properties of the induced dynamics is raised from the level of experimentally observed facts to the level of a theorem completely proved. A special family of solutions… (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)

- Gábor Péter, Szabó, Mihály Csaba, Markót, Tibor Csendes
- 2005

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)

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)

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)

The multistart clustering global optimization method called GLOBAL has been introduced in the 1980s for bound constrained global optimization problems with black-box type objective function. Since then the technological environment has been changed much. The present paper describes shortly the revisions and updates made on the involved algorithms to utilize… (More)