Numerical optimization for symmetric tensor decomposition

• 成果类型: Article; Proceedings Paper
• 署名作者: Kolda, Tamara G.
• 署名单位: United States Department of Energy (DOE); Sandia National Laboratories
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-015-0895-0
• 发表日期: 2015
• 页码: 225-248
• 关键词: algorithms; approximation; rank-1

摘要

We consider the problem of decomposing a real-valued symmetric tensor as the sum of outer products of real-valued vectors. Algebraic methods exist for computing complex-valued decompositions of symmetric tensors, but here we focus on real-valued decompositions, both unconstrained and nonnegative, for problems with low-rank structure. We discuss when solutions exist and how to formulate the mathematical program. Numerical results show the properties of the proposed formulations (including one that ignores symmetry) on a set of test problems and illustrate that these straightforward formulations can be effective even though the problem is nonconvex.