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.
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Gillard, J., Zhigljavsky, A. Optimization challenges in the structured low rank approximation problem. J Glob Optim 57, 733–751 (2013). https://doi.org/10.1007/s10898-012-9962-8
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DOI: https://doi.org/10.1007/s10898-012-9962-8