IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v96y1998i1d10.1023_a1022671302532.html
   My bibliography  Save this article

Subgradient Method with Entropic Projections for Convex Nondifferentiable Minimization

Author

Listed:
  • K. C. Kiwiel

    (Systems Research Institute)

Abstract

We replace orthogonal projections in the Polyak subgradient method for nonnegatively constrained minimization with entropic projections, thus obtaining an interior-point subgradient method. Inexact entropic projections are quite cheap. Global convergence of the resulting method is established.

Suggested Citation

  • K. C. Kiwiel, 1998. "Subgradient Method with Entropic Projections for Convex Nondifferentiable Minimization," Journal of Optimization Theory and Applications, Springer, vol. 96(1), pages 159-173, January.
    • Handle: RePEc:spr:joptap:v:96:y:1998:i:1:d:10.1023_a:1022671302532
    DOI: 10.1023/A:1022671302532
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1022671302532
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1022671302532?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. Larsson, Torbjorn & Patriksson, Michael & Stromberg, Ann-Brith, 1996. "Conditional subgradient optimization -- Theory and applications," European Journal of Operational Research, Elsevier, vol. 88(2), pages 382-403, January.
    2. Alfredo N. Iusem & B. F. Svaiter & Marc Teboulle, 1994. "Entropy-Like Proximal Methods in Convex Programming," Mathematics of Operations Research, INFORMS, vol. 19(4), pages 790-814, November.
    3. Alfredo N. Iusem & Marc Teboulle, 1995. "Convergence Rate Analysis of Nonquadratic Proximal Methods for Convex and Linear Programming," Mathematics of Operations Research, INFORMS, vol. 20(3), pages 657-677, August.
    4. Marc Teboulle, 1992. "Entropic Proximal Mappings with Applications to Nonlinear Programming," Mathematics of Operations Research, INFORMS, vol. 17(3), pages 670-690, August.
    5. Jonathan Eckstein, 1993. "Nonlinear Proximal Point Algorithms Using Bregman Functions, with Applications to Convex Programming," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 202-226, February.
    6. Marshall L. Fisher, 1985. "An Applications Oriented Guide to Lagrangian Relaxation," Interfaces, INFORMS, vol. 15(2), pages 10-21, April.
    7. Krzysztof C. Kiwiel, 1997. "Free-Steering Relaxation Methods for Problems with Strictly Convex Costs and Linear Constraints," Mathematics of Operations Research, INFORMS, vol. 22(2), pages 326-349, May.
    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. Dirk Lorenz & Marc Pfetsch & Andreas Tillmann, 2014. "An infeasible-point subgradient method using adaptive approximate projections," Computational Optimization and Applications, Springer, vol. 57(2), pages 271-306, March.
    2. A. Auslender & M. Teboulle, 2004. "Interior Gradient and Epsilon-Subgradient Descent Methods for Constrained Convex Minimization," Mathematics of Operations Research, INFORMS, vol. 29(1), pages 1-26, February.

    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. Papa Quiroz, E.A. & Roberto Oliveira, P., 2012. "An extension of proximal methods for quasiconvex minimization on the nonnegative orthant," European Journal of Operational Research, Elsevier, vol. 216(1), pages 26-32.
    2. A. Auslender & M. Teboulle, 2004. "Interior Gradient and Epsilon-Subgradient Descent Methods for Constrained Convex Minimization," Mathematics of Operations Research, INFORMS, vol. 29(1), pages 1-26, February.
    3. Regina Sandra Burachik & B. F. Svaiter, 2001. "A Relative Error Tolerance for a Family of Generalized Proximal Point Methods," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 816-831, November.
    4. Hong T. M. Chu & Ling Liang & Kim-Chuan Toh & Lei Yang, 2023. "An efficient implementable inexact entropic proximal point algorithm for a class of linear programming problems," Computational Optimization and Applications, Springer, vol. 85(1), pages 107-146, May.
    5. Jein-Shan Chen & Shaohua Pan, 2010. "An entropy-like proximal algorithm and the exponential multiplier method for convex symmetric cone programming," Computational Optimization and Applications, Springer, vol. 47(3), pages 477-499, November.
    6. A. N. Iusem, 1998. "On Some Properties of Generalized Proximal Point Methods for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 96(2), pages 337-362, February.
    7. K. Kiwiel, 1995. "Proximal Minimization Methods with Generalized Bregman Functions," Working Papers wp95024, International Institute for Applied Systems Analysis.
    8. Paul Tseng, 2004. "An Analysis of the EM Algorithm and Entropy-Like Proximal Point Methods," Mathematics of Operations Research, INFORMS, vol. 29(1), pages 27-44, February.
    9. Emanuel Laude & Peter Ochs & Daniel Cremers, 2020. "Bregman Proximal Mappings and Bregman–Moreau Envelopes Under Relative Prox-Regularity," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 724-761, March.
    10. Jonathan Eckstein & Paulo Silva, 2010. "Proximal methods for nonlinear programming: double regularization and inexact subproblems," Computational Optimization and Applications, Springer, vol. 46(2), pages 279-304, June.
    11. K. C. Kiwiel, 1998. "Generalized Bregman Projections in Convex Feasibility Problems," Journal of Optimization Theory and Applications, Springer, vol. 96(1), pages 139-157, January.
    12. Heinz H. Bauschke & Jérôme Bolte & Marc Teboulle, 2017. "A Descent Lemma Beyond Lipschitz Gradient Continuity: First-Order Methods Revisited and Applications," Mathematics of Operations Research, INFORMS, vol. 42(2), pages 330-348, May.
    13. Pinheiro, Ricardo B.N.M. & Lage, Guilherme G. & da Costa, Geraldo R.M., 2019. "A primal-dual integrated nonlinear rescaling approach applied to the optimal reactive dispatch problem," European Journal of Operational Research, Elsevier, vol. 276(3), pages 1137-1153.
    14. S. H. Pan & J. S. Chen, 2008. "Proximal-Like Algorithm Using the Quasi D-Function for Convex Second-Order Cone Programming," Journal of Optimization Theory and Applications, Springer, vol. 138(1), pages 95-113, July.
    15. Arnaldo S. Brito & J. X. Cruz Neto & Jurandir O. Lopes & P. Roberto Oliveira, 2012. "Interior Proximal Algorithm for Quasiconvex Programming Problems and Variational Inequalities with Linear Constraints," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 217-234, July.
    16. H. Attouch & M. Teboulle, 2004. "Regularized Lotka-Volterra Dynamical System as Continuous Proximal-Like Method in Optimization," Journal of Optimization Theory and Applications, Springer, vol. 121(3), pages 541-570, June.
    17. Torbjörn Larsson & Michael Patriksson, 2006. "Global Optimality Conditions for Discrete and Nonconvex Optimization---With Applications to Lagrangian Heuristics and Column Generation," Operations Research, INFORMS, vol. 54(3), pages 436-453, June.
    18. K. Kiwiel, 1994. "A Note on the Twice Differentiable Cubic Augmented Lagrangian," Working Papers wp94012, International Institute for Applied Systems Analysis.
    19. G. Bento & J. Cruz Neto & J. Lopes & A. Soares Jr & Antoine Soubeyran, 2016. "Generalized Proximal Distances for Bilevel Equilibrium Problems," Post-Print hal-01690192, HAL.
    20. K. Kiwiel, 1994. "Free-Steering Relaxation Methods for Problems with Strictly Convex Costs and Linear Constraints," Working Papers wp94089, International Institute for Applied Systems Analysis.

    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:joptap:v:96:y:1998:i:1:d:10.1023_a:1022671302532. 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.