# Optimization of Functions Given in the Tensor Train Format

arXiv: https://arxiv.org/abs/2209.14808 · HTML: https://mlsanity.com/paper/2209.14808/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Sep 2022.

## Built on by (most cited first, 7 of 7)

- [Functional Bayesian Tucker Decomposition for Continuous-indexed Tensor Data](https://mlsanity.com/paper/2311.04829/) (2023)
- [Generating Full-field Evolution of Physical Dynamics from Irregular Sparse Observations](https://mlsanity.com/paper/2505.09284/) (2025)
- [Translate your gibberish: black-box adversarial attack on machine translation systems](https://mlsanity.com/paper/2303.10974/) (2023)
- [Fast gradient-free activation maximization for neurons in spiking neural networks](https://mlsanity.com/paper/2401.10748/) (2023)
- [Functional Complexity-adaptive Temporal Tensor Decomposition](https://mlsanity.com/paper/2502.06164/) (2025)
- [StreamPhy: Streaming Inference of High-Dimensional Physical Dynamics via State Space Models](https://mlsanity.com/paper/2605.07384/) (2026)
- [Constraint-Aware Discrete Black-Box Optimization Using Tensor Decomposition](https://mlsanity.com/paper/2609.09370/) (2026)

## Abstract (arXiv)

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.