IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v147y2010i2d10.1007_s10957-010-9719-9.html
   My bibliography  Save this article

Pseudotransient Continuation for Solving Systems of Nonsmooth Equations with Inequality Constraints

Author

Listed:
  • J. Chen

    (University of Colorado Denver)

  • L. Qi

    (The Hong Kong Polytechnic University)

Abstract

This paper investigates a pseudotransient continuation algorithm for solving a system of nonsmooth equations with inequality constraints. We first transform the inequality constrained system of nonlinear equations to an augmented nonsmooth system, and then employ the pseudotransient continuation algorithm for solving the corresponding augmented nonsmooth system. The method gets its global convergence properties from the dynamics, and inherits its local convergence properties from the semismooth Newton method. Finally, we illustrate the behavior of our approach by some numerical experiments.

Suggested Citation

  • J. Chen & L. Qi, 2010. "Pseudotransient Continuation for Solving Systems of Nonsmooth Equations with Inequality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 147(2), pages 223-242, November.
    • Handle: RePEc:spr:joptap:v:147:y:2010:i:2:d:10.1007_s10957-010-9719-9
    DOI: 10.1007/s10957-010-9719-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-010-9719-9
    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/s10957-010-9719-9?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. Smale, Steve, 1976. "A convergent process of price adjustment and global newton methods," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 107-120, July.
    2. X. J. Tong & L. Qi, 2004. "On the Convergence of a Trust-Region Method for Solving Constrained Nonlinear Equations with Degenerate Solutions," Journal of Optimization Theory and Applications, Springer, vol. 123(1), pages 187-211, October.
    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. L. Qi & X. J. Tong & D. H. Li, 2004. "Active-Set Projected Trust-Region Algorithm for Box-Constrained Nonsmooth Equations," Journal of Optimization Theory and Applications, Springer, vol. 120(3), pages 601-625, March.
    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. Gonglin Yuan & Zengxin Wei & Zhongxing Wang, 2013. "Gradient trust region algorithm with limited memory BFGS update for nonsmooth convex minimization," Computational Optimization and Applications, Springer, vol. 54(1), pages 45-64, January.
    2. Leonardo Galli & Christian Kanzow & Marco Sciandrone, 2018. "A nonmonotone trust-region method for generalized Nash equilibrium and related problems with strong convergence properties," Computational Optimization and Applications, Springer, vol. 69(3), pages 629-652, April.
    3. Gonglin Yuan & Zehong Meng & Yong Li, 2016. "A Modified Hestenes and Stiefel Conjugate Gradient Algorithm for Large-Scale Nonsmooth Minimizations and Nonlinear Equations," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 129-152, January.
    4. John Duggan & Tasos Kalandrakis, 2011. "A Newton collocation method for solving dynamic bargaining games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 36(3), pages 611-650, April.
    5. H. Xu & B. M. Glover, 1997. "New Version of the Newton Method for Nonsmooth Equations," Journal of Optimization Theory and Applications, Springer, vol. 93(2), pages 395-415, May.
    6. Tuinstra, J., 2000. "Price adjustment in a model of monopolistic competition," CeNDEF Working Papers 00-13, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    7. van der Laan, G. & Talman, A.J.J., 1985. "Adjustment processes for finding economic equilibria," Research Memorandum FEW 174, Tilburg University, School of Economics and Management.
    8. Sanja Rapajić & Zoltan Papp, 2017. "A nonmonotone Jacobian smoothing inexact Newton method for NCP," Computational Optimization and Applications, Springer, vol. 66(3), pages 507-532, April.
    9. Herings, Jean-Jacques & van der Laan, Gerard & Venniker, Richard, 1998. "The transition from a Dreze equilibrium to a Walrasian equilibrium1," Journal of Mathematical Economics, Elsevier, vol. 29(3), pages 303-330, April.
    10. G. L. Zhou & L. Caccetta, 2008. "Feasible Semismooth Newton Method for a Class of Stochastic Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 379-392, November.
    11. C. Kanzow & H. Qi & L. Qi, 2003. "On the Minimum Norm Solution of Linear Programs," Journal of Optimization Theory and Applications, Springer, vol. 116(2), pages 333-345, February.
    12. Denizalp Goktas & Jiayi Zhao & Amy Greenwald, 2023. "T\^atonnement in Homothetic Fisher Markets," Papers 2306.04890, arXiv.org.
    13. Rabani, Yuval & Schulman, Leonard J., 2021. "The invisible hand of Laplace: The role of market structure in price convergence and oscillation," Journal of Mathematical Economics, Elsevier, vol. 95(C).
    14. Kenji Ueda & Nobuo Yamashita, 2012. "Global Complexity Bound Analysis of the Levenberg–Marquardt Method for Nonsmooth Equations and Its Application to the Nonlinear Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 152(2), pages 450-467, February.
    15. Anjan Mukherji, 2012. "The second fundamental theorem of positive economics," International Journal of Economic Theory, The International Society for Economic Theory, vol. 8(2), pages 125-138, June.
    16. Polyak, B.T., 2007. "Newton's method and its use in optimization," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1086-1096, September.
    17. Sjur Didrik Flåm, 2020. "Emergence of price-taking Behavior," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 847-870, October.
    18. Y. D. Chen & Y. Gao & Y.-J. Liu, 2010. "An Inexact SQP Newton Method for Convex SC1 Minimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 33-49, July.
    19. Frank Ackerman, 2001. "Still dead after all these years: interpreting the failure of general equilibrium theory," Journal of Economic Methodology, Taylor & Francis Journals, vol. 9(2), pages 119-139.
    20. Cavalli, Fausto & Naimzada, Ahmad, 2015. "A tâtonnement process with fading memory, stabilization and optimal speed of convergence," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 116-129.

    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:147:y:2010:i:2:d:10.1007_s10957-010-9719-9. 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.