IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v343y2019icp67-89.html
   My bibliography  Save this article

A two-phase-like proximal point algorithm in domains of positivity

Author

Listed:
  • Gregório, R.M.
  • Oliveira, P.R.
  • Alves, C.D.S.

Abstract

This paper improves a decomposition-like proximal point algorithm, developed for computing minima of nonsmooth convex functions within a framework of symmetric positive semidefinite matrices, and extends it to domains of positivity of reducible type, in a nonlinear sense and in a Riemannian setting. Several computational experiments with weighted Lp (p=1,2) centers of mass are performed to demonstrate the practical feasibility of the method.

Suggested Citation

  • Gregório, R.M. & Oliveira, P.R. & Alves, C.D.S., 2019. "A two-phase-like proximal point algorithm in domains of positivity," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 67-89.
    • Handle: RePEc:eee:apmaco:v:343:y:2019:i:c:p:67-89
    DOI: 10.1016/j.amc.2018.09.054
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318308336
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.09.054?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. NESTEROV , Yu. & TODD, Mike, 2002. "On the Riemannian geometry defined by self-concordant barriers and interior-point methods," LIDAM Reprints CORE 1595, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. O. P. Ferreira & P. R. Oliveira, 1998. "Subgradient Algorithm on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 97(1), pages 93-104, April.
    3. Magnus, Jan R., 1985. "On Differentiating Eigenvalues and Eigenvectors," Econometric Theory, Cambridge University Press, vol. 1(2), pages 179-191, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. da Silva Alves, Charlan Dellon & Oliveira, Paulo Roberto & Gregório, Ronaldo Malheiros, 2021. "Lα Riemannian weighted centers of mass applied to compose an image filter to diffusion tensor imaging," Applied Mathematics and Computation, Elsevier, vol. 390(C).

    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. Glaydston C. Bento & Orizon P. Ferreira & Jefferson G. Melo, 2017. "Iteration-Complexity of Gradient, Subgradient and Proximal Point Methods on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 548-562, May.
    2. E. A. Papa Quiroz & P. R. Oliveira, 2007. "New Self-Concordant Barrier for the Hypercube," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 475-490, December.
    3. G. C. Bento & O. P. Ferreira & P. R. Oliveira, 2012. "Unconstrained Steepest Descent Method for Multicriteria Optimization on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 88-107, July.
    4. Broda, S. & Paolella, M.S., 2009. "Evaluating the density of ratios of noncentral quadratic forms in normal variables," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1264-1270, February.
    5. Wiens, Douglas P., 2021. "Robust designs for dose–response studies: Model and labelling robustness," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    6. João Carlos de O. Souza, 2018. "Proximal Point Methods for Lipschitz Functions on Hadamard Manifolds: Scalar and Vectorial Cases," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 745-760, December.
    7. J. X. Cruz Neto & O. P. Ferreira & P. R. Oliveira & R. C. M. Silva, 2008. "Central Paths in Semidefinite Programming, Generalized Proximal-Point Method and Cauchy Trajectories in Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 227-242, November.
    8. da Silva Alves, Charlan Dellon & Oliveira, Paulo Roberto & Gregório, Ronaldo Malheiros, 2021. "Lα Riemannian weighted centers of mass applied to compose an image filter to diffusion tensor imaging," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    9. T. Bittencourt & O. P. Ferreira, 2017. "Kantorovich’s theorem on Newton’s method under majorant condition in Riemannian manifolds," Journal of Global Optimization, Springer, vol. 68(2), pages 387-411, June.
    10. Erik Alex Papa Quiroz & Nancy Baygorrea Cusihuallpa & Nelson Maculan, 2020. "Inexact Proximal Point Methods for Multiobjective Quasiconvex Minimization on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 879-898, September.
    11. Glaydston Carvalho Bento & Sandro Dimy Barbosa Bitar & João Xavier Cruz Neto & Paulo Roberto Oliveira & João Carlos Oliveira Souza, 2019. "Computing Riemannian Center of Mass on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 977-992, December.
    12. Liu, Shuangzhe & Leiva, Víctor & Zhuang, Dan & Ma, Tiefeng & Figueroa-Zúñiga, Jorge I., 2022. "Matrix differential calculus with applications in the multivariate linear model and its diagnostics," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    13. J. X. Cruz Neto & F. M. O. Jacinto & P. A. Soares & J. C. O. Souza, 2018. "On maximal monotonicity of bifunctions on Hadamard manifolds," Journal of Global Optimization, Springer, vol. 72(3), pages 591-601, November.
    14. David Baqaee & Emmanuel Farhi & Michael J. Mina & James H. Stock, 2020. "Reopening Scenarios," NBER Working Papers 27244, National Bureau of Economic Research, Inc.
    15. Peng Zhang & Gejun Bao, 2018. "An Incremental Subgradient Method on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 711-727, March.
    16. Lei Wang & Xin Liu & Yin Zhang, 2023. "A communication-efficient and privacy-aware distributed algorithm for sparse PCA," Computational Optimization and Applications, Springer, vol. 85(3), pages 1033-1072, July.
    17. Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2013. "Nonparametric estimation of finite mixtures," SciencePo Working papers hal-00972868, HAL.
    18. Guohua Feng & Apostolos Serletis, 2009. "Efficiency and productivity of the US banking industry, 1998-2005: evidence from the Fourier cost function satisfying global regularity conditions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(1), pages 105-138.
    19. Eduardo Abi Jaber & Bruno Bouchard & Camille Illand & Eduardo Jaber, 2018. "Stochastic invariance of closed sets with non-Lipschitz coefficients," Working Papers hal-01349639, HAL.
    20. Dovonon, Prosper & Taamouti, Abderrahim & Williams, Julian, 2022. "Testing the eigenvalue structure of spot and integrated covariance," Journal of Econometrics, Elsevier, vol. 229(2), pages 363-395.

    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:eee:apmaco:v:343:y:2019:i:c:p:67-89. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.