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MiS Preprint

Optimization Problems in Contracted Tensor Networks

Mike Espig, Wolfgang Hackbusch, Stefan Handschuh and Reinhold Schneider


We discuss the calculus of variations in tensor representations with a special focus on tensor networks and apply it to functionals of practical interest. The survey provides all necessary ingredients for applying minimization methods in a general setting. The important cases of target functionals which are linear and quadratic with respect to the tensor product are discussed, and combinations of these functionals are presented in detail. As an example, we consider the representation rank compression in tensor networks. For the numerical treatment, we use the nonlinear block Gauss-Seidel method. We demonstrate the rate of convergence in numerical tests.

Oct 17, 2011
Oct 18, 2011

Related publications

2011 Repository Open Access
Mike Espig, Wolfgang Hackbusch, Stefan Handschuh and Reinhold Schneider

Optimization problems in contracted tensor networks

In: Computing and visualization in science, 14 (2011) 6, pp. 271-285