On Local Convergence of Alternating Schemes for Optimization of Convex Problems in the Tensor Train Format

By Thorsten Rohwedder, André Uschmajew. 2013

116 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Computational Mathematics, Computational Theory and Mathematics

How researchers see this paper

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

In Atomic and Molecular Physics, and Optics

1. Dmitry V. Savostyanov
2. Qibin Zhao
3. Andrzej S. Cichocki
4. Guoxu Zhou
5. André Uschmajew
6. V. Dolgov
7. Ivan V. Oseledets
8. Boris N. Khoromskij

In Computational Mathematics

1. Andrzej S. Cichocki
2. Qibin Zhao
3. V. Dolgov
4. Guoxu Zhou
5. Liqing Zhang
6. Dmitry V. Savostyanov
7. André Uschmajew
8. Shengli Xie

In Computational Theory and Mathematics

1. Andrzej S. Cichocki
2. Qibin Zhao
3. V. Dolgov
4. Dmitry V. Savostyanov
5. Guoxu Zhou
6. André Uschmajew
7. Liqing Zhang
8. Shengli Xie

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 [227].”
• Low-rank methods for high-dimensional approximation and model order reduction (2015, unknown): “FSr(p1,...,pM) from Pi to X). The available convergence results for these optimization algorithms in a general setting only ensure local convergence or global convergence to critical points (see e.g. [74, 36]). 3.4 Higher-order singular value decomposition The Higher-Order Singular Value Decompositi”
• Tensor product methods and entanglement optimization for ab initio quantum chemistry (2014, unknown): “〈μ ‖ ci ‖ ν〉 = 0 0 0 1 0 0 0 − √ 2 0  , (203)”
• Zur Theorie der Niedrigrangapproximation in Tensorprodukten von Hilberträumen (2013, background): “Die Darstellung ist alles andere als erschöpfend, sondern orientiert sich lose an den im Literaturverzeichnis gelisteten Arbeiten des Autors.”
• Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions (2013, unknown): “However, its theoretical understanding is still very limited, and only local convergence estimates for the simplest one-site DMRG algorithm, also known as the alternating linear scheme (ALS), are available [49].”
• ALTERNATING MINIMAL ENERGY METHODS FOR LINEAR SYSTEMS IN HIGHER DIMENSIONS∗ (2014, background): “However, its theoretical understanding is still very limited, and only local convergence estimates for the simplest one-site DMRG algorithm, also known as the alternating linear scheme (ALS), are available [49].”
• Tensor Ring Decomposition (2016, methodology): “In [32], [47], TT decomposition is optimized by a suitable generalization of the alternating least squares (ALS) algorithm and modified ALS (MALS) algorithm which facilitates the self-adaptation of ranks either by using SVDs or by employing a greedy algo-rithm.”