IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v46y2010i2p279-304.html
   My bibliography  Save this article

Proximal methods for nonlinear programming: double regularization and inexact subproblems

Author

Listed:
  • Jonathan Eckstein
  • Paulo Silva

Abstract

No abstract is available for this item.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:46:y:2010:i:2:p:279-304
    DOI: 10.1007/s10589-009-9274-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10589-009-9274-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10589-009-9274-1?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. Marc Teboulle, 1992. "Entropic Proximal Mappings with Applications to Nonlinear Programming," Mathematics of Operations Research, INFORMS, vol. 17(3), pages 670-690, August.
    2. 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.
    3. Liqun Qi, 1993. "Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 227-244, February.
    4. R. T. Rockafellar, 1976. "Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 97-116, May.
    5. Alfred Auslender & Marc Teboulle & Sami Ben-Tiba, 1999. "Interior Proximal and Multiplier Methods Based on Second Order Homogeneous Kernels," Mathematics of Operations Research, INFORMS, vol. 24(3), pages 645-668, August.
    6. Teemu Pennanen, 2002. "Local Convergence of the Proximal Point Algorithm and Multiplier Methods Without Monotonicity," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 170-191, February.
    7. M. V. Solodov & B. F. Svaiter, 2000. "An Inexact Hybrid Generalized Proximal Point Algorithm and Some New Results on the Theory of Bregman Functions," Mathematics of Operations Research, INFORMS, vol. 25(2), pages 214-230, 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. Nils Langenberg, 2015. "Interior Proximal Method Without the Cutting Plane Property," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 529-557, August.

    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. 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.
    3. 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.
    4. M. Kyono & M. Fukushima, 2000. "Nonlinear Proximal Decomposition Method for Convex Programming," Journal of Optimization Theory and Applications, Springer, vol. 106(2), pages 357-372, August.
    5. 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.
    6. Papa Quiroz, E.A. & Mallma Ramirez, L. & Oliveira, P.R., 2015. "An inexact proximal method for quasiconvex minimization," European Journal of Operational Research, Elsevier, vol. 246(3), pages 721-729.
    7. Souza, Sissy da S. & Oliveira, P.R. & da Cruz Neto, J.X. & Soubeyran, A., 2010. "A proximal method with separable Bregman distances for quasiconvex minimization over the nonnegative orthant," European Journal of Operational Research, Elsevier, vol. 201(2), pages 365-376, March.
    8. 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.
    9. Liang Chen & Anping Liao, 2020. "On the Convergence Properties of a Second-Order Augmented Lagrangian Method for Nonlinear Programming Problems with Inequality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 187(1), pages 248-265, October.
    10. Bingsheng He & Li-Zhi Liao & Xiang Wang, 2012. "Proximal-like contraction methods for monotone variational inequalities in a unified framework I: Effective quadruplet and primary methods," Computational Optimization and Applications, Springer, vol. 51(2), pages 649-679, March.
    11. 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.
    12. 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.
    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. Bingsheng He & Li-Zhi Liao & Xiang Wang, 2012. "Proximal-like contraction methods for monotone variational inequalities in a unified framework II: general methods and numerical experiments," Computational Optimization and Applications, Springer, vol. 51(2), pages 681-708, March.
    15. Francisco Aragón Artacho & Michaël Gaydu, 2012. "A Lyusternik–Graves theorem for the proximal point method," Computational Optimization and Applications, Springer, vol. 52(3), pages 785-803, July.
    16. Spyridon Pougkakiotis & Jacek Gondzio, 2021. "An interior point-proximal method of multipliers for convex quadratic programming," Computational Optimization and Applications, Springer, vol. 78(2), pages 307-351, March.
    17. Volkovich, Vladimir & Kogan, Jacob & Nicholas, Charles, 2007. "Building initial partitions through sampling techniques," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1097-1105, December.
    18. 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.
    19. 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.
    20. 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.

    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:46:y:2010:i:2:p:279-304. 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.