IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v86y2023i1d10.1007_s10589-023-00490-3.html
   My bibliography  Save this article

Average curvature FISTA for nonconvex smooth composite optimization problems

Author

Listed:
  • Jiaming Liang

    (Yale University)

  • Renato D. C. Monteiro

    (Georgia Institute of Technology)

Abstract

A previous authors’ paper introduces an accelerated composite gradient (ACG) variant, namely AC-ACG, for solving nonconvex smooth composite optimization (N-SCO) problems. In contrast to other ACG variants, AC-ACG estimates the local upper curvature of the N-SCO problem by using the average of the observed upper-Lipschitz curvatures obtained during the previous iterations, and uses this estimation and two composite resolvent evaluations to compute the next iterate. This paper presents an alternative FISTA-type ACG variant, namely AC-FISTA, which has the following additional features: (i) it performs an average of one composite resolvent evaluation per iteration; and (ii) it estimates the local upper curvature by using the average of the previously observed upper (instead of upper-Lipschitz) curvatures. These two properties acting together yield a practical AC-FISTA variant which substantially outperforms earlier ACG variants, including the AC-ACG variants discussed in the aforementioned authors’ paper.

Suggested Citation

  • Jiaming Liang & Renato D. C. Monteiro, 2023. "Average curvature FISTA for nonconvex smooth composite optimization problems," Computational Optimization and Applications, Springer, vol. 86(1), pages 275-302, September.
    • Handle: RePEc:spr:coopap:v:86:y:2023:i:1:d:10.1007_s10589-023-00490-3
    DOI: 10.1007/s10589-023-00490-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-023-00490-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10589-023-00490-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jiaming Liang & Renato D. C. Monteiro & Chee-Khian Sim, 2021. "A FISTA-type accelerated gradient algorithm for solving smooth nonconvex composite optimization problems," Computational Optimization and Applications, Springer, vol. 79(3), pages 649-679, July.
    2. Daniel D. Lee & H. Sebastian Seung, 1999. "Learning the parts of objects by non-negative matrix factorization," Nature, Nature, vol. 401(6755), pages 788-791, October.
    3. Weiwei Kong & Renato D. C. Monteiro, 2022. "Accelerated inexact composite gradient methods for nonconvex spectral optimization problems," Computational Optimization and Applications, Springer, vol. 82(3), pages 673-715, July.
    Full references (including those not matched with items on IDEAS)

    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.
    1. Del Corso, Gianna M. & Romani, Francesco, 2019. "Adaptive nonnegative matrix factorization and measure comparisons for recommender systems," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 164-179.
    2. P Fogel & C Geissler & P Cotte & G Luta, 2022. "Applying separative non-negative matrix factorization to extra-financial data," Working Papers hal-03689774, HAL.
    3. Xiao-Bai Li & Jialun Qin, 2017. "Anonymizing and Sharing Medical Text Records," Information Systems Research, INFORMS, vol. 28(2), pages 332-352, June.
    4. Naiyang Guan & Lei Wei & Zhigang Luo & Dacheng Tao, 2013. "Limited-Memory Fast Gradient Descent Method for Graph Regularized Nonnegative Matrix Factorization," PLOS ONE, Public Library of Science, vol. 8(10), pages 1-10, October.
    5. Spelta, A. & Pecora, N. & Rovira Kaltwasser, P., 2019. "Identifying Systemically Important Banks: A temporal approach for macroprudential policies," Journal of Policy Modeling, Elsevier, vol. 41(1), pages 197-218.
    6. M. Moghadam & K. Aminian & M. Asghari & M. Parnianpour, 2013. "How well do the muscular synergies extracted via non-negative matrix factorisation explain the variation of torque at shoulder joint?," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 16(3), pages 291-301.
    7. Markovsky, Ivan & Niranjan, Mahesan, 2010. "Approximate low-rank factorization with structured factors," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3411-3420, December.
    8. Paul Fogel & Yann Gaston-Mathé & Douglas Hawkins & Fajwel Fogel & George Luta & S. Stanley Young, 2016. "Applications of a Novel Clustering Approach Using Non-Negative Matrix Factorization to Environmental Research in Public Health," IJERPH, MDPI, vol. 13(5), pages 1-14, May.
    9. Le Thi Khanh Hien & Duy Nhat Phan & Nicolas Gillis, 2022. "Inertial alternating direction method of multipliers for non-convex non-smooth optimization," Computational Optimization and Applications, Springer, vol. 83(1), pages 247-285, September.
    10. Chae, Bongsug (Kevin), 2018. "The Internet of Things (IoT): A Survey of Topics and Trends using Twitter Data and Topic Modeling," 22nd ITS Biennial Conference, Seoul 2018. Beyond the boundaries: Challenges for business, policy and society 190376, International Telecommunications Society (ITS).
    11. Jingfeng Guo & Chao Zheng & Shanshan Li & Yutong Jia & Bin Liu, 2022. "BiInfGCN: Bilateral Information Augmentation of Graph Convolutional Networks for Recommendation," Mathematics, MDPI, vol. 10(17), pages 1-16, August.
    12. Jianfei Cao & Han Yang & Jianshu Lv & Quanyuan Wu & Baolei Zhang, 2023. "Estimating Soil Salinity with Different Levels of Vegetation Cover by Using Hyperspectral and Non-Negative Matrix Factorization Algorithm," IJERPH, MDPI, vol. 20(4), pages 1-15, February.
    13. Wang, Ketong & Porter, Michael D., 2018. "Optimal Bayesian clustering using non-negative matrix factorization," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 395-411.
    14. Semi Min & Juyong Park, 2019. "Modeling narrative structure and dynamics with networks, sentiment analysis, and topic modeling," PLOS ONE, Public Library of Science, vol. 14(12), pages 1-20, December.
    15. Zhang, Lifeng & Chao, Xiangrui & Qian, Qian & Jing, Fuying, 2022. "Credit evaluation solutions for social groups with poor services in financial inclusion: A technical forecasting method," Technological Forecasting and Social Change, Elsevier, vol. 183(C).
    16. Wentao Qu & Xianchao Xiu & Huangyue Chen & Lingchen Kong, 2023. "A Survey on High-Dimensional Subspace Clustering," Mathematics, MDPI, vol. 11(2), pages 1-39, January.
    17. Anna Luiza Silva Almeida Vicente & Alexei Novoloaca & Vincent Cahais & Zainab Awada & Cyrille Cuenin & Natália Spitz & André Lopes Carvalho & Adriane Feijó Evangelista & Camila Souza Crovador & Rui Ma, 2022. "Cutaneous and acral melanoma cross-OMICs reveals prognostic cancer drivers associated with pathobiology and ultraviolet exposure," Nature Communications, Nature, vol. 13(1), pages 1-15, December.
    18. Guillote, Simon & Perron, Francois & Segers, Johan, 2018. "Bayesian Inference For Bivariate Ranks," LIDAM Discussion Papers ISBA 2018005, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    19. Takehiro Sano & Tsuyoshi Migita & Norikazu Takahashi, 2022. "A novel update rule of HALS algorithm for nonnegative matrix factorization and Zangwill’s global convergence," Journal of Global Optimization, Springer, vol. 84(3), pages 755-781, November.
    20. Adam R. Pines & Bart Larsen & Zaixu Cui & Valerie J. Sydnor & Maxwell A. Bertolero & Azeez Adebimpe & Aaron F. Alexander-Bloch & Christos Davatzikos & Damien A. Fair & Ruben C. Gur & Raquel E. Gur & H, 2022. "Dissociable multi-scale patterns of development in personalized brain networks," Nature Communications, Nature, vol. 13(1), pages 1-15, December.

    Corrections

    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:coopap:v:86:y:2023:i:1:d:10.1007_s10589-023-00490-3. 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.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.