Tensor train (TT) format is a common approach for computationally efficient work with multidimensional arrays, vectors, matrices, and discretized functions in a wide range of applications, including computational mathematics and machine learning. In this work, we propose a new algorithm for TT-tensor optimization, which leads to very accurate approximations for the minimum and maximum tensor element. The method consists in sequential tensor multiplications of the TT-cores with an intelligent selection of candidates for the optimum. We propose the probabilistic interpretation of the method, and make estimates on its complexity and convergence. We perform extensive numerical experiments with random tensors and various multivariable benchmark functions with the number of input dimensions up to $100$. Our approach generates a solution close to the exact optimum for all model problems, while the running time is no more than $50$ seconds on a regular laptop.

翻译：Tensor train (TT) 格式是一种通用的方法,用于计算多面阵列、矢量、矩阵和在包括计算数学和机器学习在内的多种应用中分解函数的高效计算工作。 在这项工作中,我们提出了一个新的TT-tensor优化算法,该算法导致最小和最大振幅元素的非常精确近似值。该方法包括TT-核心的相继增法,并明智地选择最佳候选人。我们提出了该方法的概率解释,并估计了其复杂性和趋同性。我们用随机的计数器和各种多变量基准函数进行了广泛的数字实验,输入维度达到100美元。我们的方法产生了一种接近于所有模型问题准确最佳的解决方案,而运行时间不超过常规膝上50美元秒。