Optimization challlenges in the structured low rank approximation problem

Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X and Zhigljavsky, Anatoly Alexandrovich ORCID: https://orcid.org/0000-0003-0630-8279 2013. Optimization challlenges in the structured low rank approximation problem. Journal of Global Optimization 57 (3) , pp. 733-751. 10.1007/s10898-012-9962-8

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Abstract

In this paper we illustrate some optimization challenges in the structured low rank approximation (SLRA) problem. SLRA can be described as the problem of finding a low rank approximation of an observed matrix which has the same structure as this matrix (such as Hankel). We demonstrate that the optimization problem arising is typically very difficult: in particular, the objective function is multiextremal even for simple cases. The main theme of the paper is to suggest that the difficulties described in approximating a solution of the SLRA problem open huge possibilities for the application of stochastic methods of global optimization.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Springer
ISSN:	0925-5001
Last Modified:	20 Oct 2022 09:48
URI:	https://orca.cardiff.ac.uk/id/eprint/33151

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