A variational approach of the rank function
Author
Abstract
Suggested Citation
DOI: 10.1007/s11750-013-0283-y
Download full text from publisher
As the access to this document is restricted, you may want to search for a different version of it.
References listed on IDEAS
- Bomze, Immanuel M., 2012. "Copositive optimization – Recent developments and applications," European Journal of Operational Research, Elsevier, vol. 216(3), pages 509-520.
- Carl Eckart & Gale Young, 1936. "The approximation of one matrix by another of lower rank," Psychometrika, Springer;The Psychometric Society, vol. 1(3), pages 211-218, September.
- Jean-Baptiste Hiriart-Urruty & Jérôme Malick, 2012. "A Fresh Variational-Analysis Look at the Positive Semidefinite Matrices World," Journal of Optimization Theory and Applications, Springer, vol. 153(3), pages 551-577, June.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
Cited by:
- Roger Behling & Douglas S. Gonçalves & Sandra A. Santos, 2019. "Local Convergence Analysis of the Levenberg–Marquardt Framework for Nonzero-Residue Nonlinear Least-Squares Problems Under an Error Bound Condition," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 1099-1122, December.
- Liqun Qi & Ziyan Luo & Qing-Wen Wang & Xinzhen Zhang, 2022. "Quaternion Matrix Optimization: Motivation and Analysis," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 621-648, June.
- Kim Christensen & Mikkel Slot Nielsen & Mark Podolskij, 2021. "High-dimensional estimation of quadratic variation based on penalized realized variance," Papers 2103.03237, arXiv.org.
- Tim Hoheisel & Elliot Paquette, 2023. "Uniqueness in Nuclear Norm Minimization: Flatness of the Nuclear Norm Sphere and Simultaneous Polarization," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 252-276, April.
Most related items
These are the items that most often cite the same works as this one and are cited by the same works as this one.- Sewell, Daniel K., 2018. "Visualizing data through curvilinear representations of matrices," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 255-270.
- Kohei Adachi & Nickolay T. Trendafilov, 2016. "Sparse principal component analysis subject to prespecified cardinality of loadings," Computational Statistics, Springer, vol. 31(4), pages 1403-1427, December.
- Norman Cliff, 1962. "Analytic rotation to a functional relationship," Psychometrika, Springer;The Psychometric Society, vol. 27(3), pages 283-295, September.
- Jushan Bai & Serena Ng, 2020. "Simpler Proofs for Approximate Factor Models of Large Dimensions," Papers 2008.00254, arXiv.org.
- Adele Ravagnani & Fabrizio Lillo & Paola Deriu & Piero Mazzarisi & Francesca Medda & Antonio Russo, 2024. "Dimensionality reduction techniques to support insider trading detection," Papers 2403.00707, arXiv.org, revised May 2024.
- Alfredo García-Hiernaux & José Casals & Miguel Jerez, 2012.
"Estimating the system order by subspace methods,"
Computational Statistics, Springer, vol. 27(3), pages 411-425, September.
- García-Hiernaux, Alfredo & Casals, José & Jerez, Miguel, 2007. "Estimating the system order by subspace methods," DES - Working Papers. Statistics and Econometrics. WS ws070301, Universidad Carlos III de Madrid. Departamento de EstadÃstica.
- Mitzi Cubilla‐Montilla & Ana‐Belén Nieto‐Librero & Ma Purificación Galindo‐Villardón & Ma Purificación Vicente Galindo & Isabel‐María Garcia‐Sanchez, 2019. "Are cultural values sufficient to improve stakeholder engagement human and labour rights issues?," Corporate Social Responsibility and Environmental Management, John Wiley & Sons, vol. 26(4), pages 938-955, July.
- Stegeman, Alwin, 2016. "A new method for simultaneous estimation of the factor model parameters, factor scores, and unique parts," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 189-203.
- Jos Berge & Henk Kiers, 1993. "An alternating least squares method for the weighted approximation of a symmetric matrix," Psychometrika, Springer;The Psychometric Society, vol. 58(1), pages 115-118, March.
- Shimeng Huang & Henry Wolkowicz, 2018. "Low-rank matrix completion using nuclear norm minimization and facial reduction," Journal of Global Optimization, Springer, vol. 72(1), pages 5-26, September.
- Antti J. Tanskanen & Jani Lukkarinen & Kari Vatanen, 2016. "Random selection of factors preserves the correlation structure in a linear factor model to a high degree," Papers 1604.05896, arXiv.org, revised Dec 2018.
- Ali Habibnia & Esfandiar Maasoumi, 2021.
"Forecasting in Big Data Environments: An Adaptable and Automated Shrinkage Estimation of Neural Networks (AAShNet),"
Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 363-381, December.
- Ali Habibnia & Esfandiar Maasoumi, 2019. "Forecasting in Big Data Environments: an Adaptable and Automated Shrinkage Estimation of Neural Networks (AAShNet)," Papers 1904.11145, arXiv.org.
- Andrey Afonin & Roland Hildebrand & Peter J. C. Dickinson, 2021. "The extreme rays of the $$6\times 6$$ 6 × 6 copositive cone," Journal of Global Optimization, Springer, vol. 79(1), pages 153-190, January.
- Jin-Xing Liu & Yong Xu & Chun-Hou Zheng & Yi Wang & Jing-Yu Yang, 2012. "Characteristic Gene Selection via Weighting Principal Components by Singular Values," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-10, July.
- Kargin, V. & Onatski, A., 2008.
"Curve forecasting by functional autoregression,"
Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2508-2526, November.
- A. Onatski & V. Karguine, 2005. "Curve Forecasting by Functional Autoregression," Computing in Economics and Finance 2005 59, Society for Computational Economics.
- Yoshio Takane & Forrest Young & Jan Leeuw, 1977. "Nonmetric individual differences multidimensional scaling: An alternating least squares method with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 42(1), pages 7-67, March.
- Aldrin, Magne, 1996. "Moderate projection pursuit regression for multivariate response data," Computational Statistics & Data Analysis, Elsevier, vol. 21(5), pages 501-531, May.
- W. Gibson, 1962. "On the least-squares orthogonalization of an oblique transformation," Psychometrika, Springer;The Psychometric Society, vol. 27(2), pages 193-195, June.
- Gordana Ispirova & Tome Eftimov & Barbara Koroušić Seljak, 2020. "P-NUT: Predicting NUTrient Content from Short Text Descriptions," Mathematics, MDPI, vol. 8(10), pages 1-21, October.
- Chester Harris, 1955. "Separation of data as a principle in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 20(1), pages 23-28, March.
More about this item
Keywords
Rank of matrix; Optimization; Nonsmooth analysis; Moreau–Yosida regularization; Generalized subdifferentials; 49-02; 65K10;All these keywords.
JEL classification:
Statistics
Access and download statisticsCorrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:topjnl:v:21:y:2013:i:2:p:207-240. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .
Please note that corrections may take a couple of weeks to filter through the various RePEc services.