Abstract--ZusammenfassungNew Results on Verified Global Optimization. We study the influence of different strategies for selecting the next box for subdivision in an interval branch and bound method for global optimization. A theoretical result establishes the optimality of a 'best-first' strategy. Moreover, we define a multisection algorithm for subdivision of boxes. Different possibilities for the choice of bisection directions and the number of bisections are compared by numerical results showing that multisection is usually superior to bisection. In addition, we identify crucial properties of a division strategy which yield convergence of an algorithm with multisection. AMS Subject Classification: 65K05.Key words: Global optimization, interval arithmetic, branch and bound principle, best-first strategy, multisection. Neue Ergebnisse bei der verifizierten globalen

We present a new parallel method for verified global optimization, using a centralized mediator for the dynamic load balancing. The new approach combines the advantages of two previous models, the master slave model and the processor farm. Numerical results show the efficiency of this new method. For a large number of problems at least linear speedup is reached. The efficiency of this new method is also confirmed by a comparison with other parallel methods for verified global optimization. A theoretical study proves that using the best-first strategy to choose the next box for subdivision, no real superlinear speedup may be expected concerning the number of iterations. Moreover, the potential of parallelization of methods of verified global optimization is discussed in general.

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