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On the worst-case optimal multi-objective global optimization

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Multi-objective optimization problem with Lipshitz objective functions is considered. It is shown that the worst-case optimal passive algorithm can be reduced to the computation of centers of balls producing the optimal cover of a feasible region, where the balls are of equal minimum radius. It is also shown, that in the worst-case, adaptivity does not improve the guaranteed accuracy achievable by the passive algorithm.

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This research is supported by the Research Council of Lithuania under Grant No. MIP-063/2012. The constructive remarks of two referees facilitated a significant improvement of the presentation of results.

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Correspondence to Antanas Žilinskas.

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Žilinskas, A. On the worst-case optimal multi-objective global optimization. Optim Lett 7, 1921–1928 (2013).

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