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In contrast to many other heuristic and stochastic methods, the global optimization based on TT-decomposition uses the structure of the optimized functional and hence allows one to obtain the global optimum in some problem faster and more reliable. The method is based on the TT-cross method of interpolation of tensors. In this case, the global optimum can be found in practice even in the case when the approximation of the tensor does not possess a high accuracy. We present a detailed description of the method and its justification for the matrix case and rank-1 approximation.