Optimization via Separated Representations and the Canonical Tensor Decomposition

TL;DR

This paper presents a new quadratically convergent algorithm for efficiently finding maximum absolute entries in tensors and global maxima of non-convex functions in separated form, with demonstrated practical performance.

Contribution

It introduces a novel, efficient algorithm for tensor optimization and global maxima detection in separated representations, improving convergence and computational complexity.

Findings

Algorithm achieves quadratic convergence.

Computational complexity is linear in tensor dimension.

Demonstrated effectiveness on multiple examples.

Abstract

We introduce a new, quadratically convergent algorithm for finding maximum absolute value entries of tensors represented in the canonical format. The computational complexity of the algorithm is linear in the dimension of the tensor. We show how to use this algorithm to find global maxima of non-convex multivariate functions in separated form. We demonstrate the performance of the new algorithms on several examples.