LOCAL CONVERGENCE OF ALTERNATING SCHEMES FOR OPTIMIZATION OF CONVEX PROBLEMS IN THE TT FORMAT

By Thorsten Rohwedder, André Uschmajew. 2011

Subfields: Optimization & Training, Mathematical Optimization

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Optimization & Training

1. Christoph Schwab
2. Michael Nip
3. Mustafa Hani Khammash
4. Vladimir A. Kazeev
5. Dmitry V. Savostyanov
6. Boris N. Khoromskij
7. Sergey V. Dolgov

In Mathematical Optimization

1. Sergey V. Dolgov
2. Dmitry V. Savostyanov
3. Vladimir A. Kazeev
4. Christoph Schwab
5. Michael Nip
6. Mustafa Hani Khammash
7. V. Dolgov
8. Boris N. Khoromskij

Citations in the corpus

• A literature survey of low‐rank tensor approximation techniques (2013, neutral): “The convergence of ALS for the TT decomposition has been studied in [226].”
• Direct Solution of the Chemical Master Equation Using Quantized Tensor Trains (2014, methodology): “In [75] a closely related Alternating Least Squares (ALS) approach was mathematically analyzed and shown to converge locally.”
• Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions (2013, unknown): “It brings the notations in consistence with previous papers on the numerical tensor methods, e.g. [18, 9, 8, 35] and others.”
• ALTERNATING MINIMAL ENERGY METHODS FOR LINEAR SYSTEMS IN HIGHER DIMENSIONS∗ (2014, background): “The DMRG/MPS schemes are very efficient but very difficult to analyse, and at the moment only local convergence results for the simplest algorithm are available [10].”
• Tensor-product approach to global time-space-parametric discretization of chemical master equation (2012, background): “There are only local estimates [53], which might be too restrictive in practice.”