
Optimization landscape of Tucker decomposition
Publication
, Journal Article
Frandsen, A; Ge, R
Published in: Mathematical Programming
June 1, 2022
Tucker decomposition is a popular technique for many data analysis and machine learning applications. Finding a Tucker decomposition is a nonconvex optimization problem. As the scale of the problems increases, local search algorithms such as stochastic gradient descent have become popular in practice. In this paper, we characterize the optimization landscape of the Tucker decomposition problem. In particular, we show that if the tensor has an exact Tucker decomposition, for a standard nonconvex objective of Tucker decomposition, all local minima are also globally optimal. We also give a local search algorithm that can find an approximate local (and global) optimal solution in polynomial time.
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Published In
Mathematical Programming
DOI
EISSN
1436-4646
ISSN
0025-5610
Publication Date
June 1, 2022
Volume
193
Issue
2
Start / End Page
687 / 712
Related Subject Headings
- Operations Research
- 4903 Numerical and computational mathematics
- 4901 Applied mathematics
- 4613 Theory of computation
- 0802 Computation Theory and Mathematics
- 0103 Numerical and Computational Mathematics
- 0102 Applied Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Frandsen, A., & Ge, R. (2022). Optimization landscape of Tucker decomposition. Mathematical Programming, 193(2), 687–712. https://doi.org/10.1007/s10107-020-01531-z
Frandsen, A., and R. Ge. “Optimization landscape of Tucker decomposition.” Mathematical Programming 193, no. 2 (June 1, 2022): 687–712. https://doi.org/10.1007/s10107-020-01531-z.
Frandsen A, Ge R. Optimization landscape of Tucker decomposition. Mathematical Programming. 2022 Jun 1;193(2):687–712.
Frandsen, A., and R. Ge. “Optimization landscape of Tucker decomposition.” Mathematical Programming, vol. 193, no. 2, June 2022, pp. 687–712. Scopus, doi:10.1007/s10107-020-01531-z.
Frandsen A, Ge R. Optimization landscape of Tucker decomposition. Mathematical Programming. 2022 Jun 1;193(2):687–712.

Published In
Mathematical Programming
DOI
EISSN
1436-4646
ISSN
0025-5610
Publication Date
June 1, 2022
Volume
193
Issue
2
Start / End Page
687 / 712
Related Subject Headings
- Operations Research
- 4903 Numerical and computational mathematics
- 4901 Applied mathematics
- 4613 Theory of computation
- 0802 Computation Theory and Mathematics
- 0103 Numerical and Computational Mathematics
- 0102 Applied Mathematics