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Tensor train (TT) format is a common approach for computationally efficientwork with multidimensional arrays, vectors, matrices, and discretized functionsin a wide range of applications, including computational mathematics andmachine learning. In this work, we propose a new algorithm for TT-tensoroptimization, which leads to very accurate approximations for the minimum andmaximum tensor element. The method consists in sequential tensormultiplications of the TT-cores with an intelligent selection of candidates forthe optimum. We propose the probabilistic interpretation of the method, andmake estimates on its complexity and convergence. We perform extensivenumerical experiments with random tensors and various multivariable benchmarkfunctions with the number of input dimensions up to $100$. Our approachgenerates a solution close to the exact optimum for all model problems, whilethe running time is no more than $50$ seconds on a regular laptop.

Optimization of Functions Given in the Tensor Train Format