Optimization via separated representations and the canonical tensor decomposition

JOURNAL OF COMPUTATIONAL PHYSICS

卷:348

Article

Reynolds, Matthew J.¹  Beylkin, Gregory²  Doostan, Alireza¹ 

[1] Univ Colorado, Dept Aerosp Engn Sci, 429 UCB, Boulder, CO 80309 USA

[2] Univ Colorado, Dept Appl Math, UCB 526, Boulder, CO 80309 USA

关键词: Separated representations;    Tensor decompositions;    Canonical tensors;    Global optimization;    Quadratic convergence;   

DOI  :  10.1016/j.jcp.2017.07.012

来源: Elsevier

【 摘 要 】

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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free