In this paper, the global optimization problem min F(y) in S with S being a hyperinterval in\udR^N and F(y) satisfying the Lipschitz condition with an unknown Lipschitz constant is considered. It is supposed that the function F(y) can be multiextremal, non-differentiable, and\udgiven as a ‘black-box’. To attack the problem, a new global optimization algorithm based on the following two ideas is proposed and studied both theoretically and numerically. First,\udthe new algorithm uses numerical approximations to space-filling curves to reduce the original Lipschitz multi-dimensional problem to a univariate one satisfying the Hölder condition. Second, the algorithm at each iteration applies a new geometric technique working\udwith a number of possible Hölder constants chosen from a set of values varying from zero to infinity showing so that ideas introduced in a popular DIRECT method can be used in the Hölder global optimization. Convergence conditions of the resulting deterministic global\udoptimization method are established. Numerical experiments carried out on several hundreds of test functions show quite a promising performance of the new algorithm in\udcomparison with its direct competitors.
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