Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

An example of irregular convergence in some constrained optimization methods that use the projected hessian

  • Published:
Mathematical Programming Submit manuscript

Abstract

In this paper we give examples illustrating the behavior of the Coleman-Conn horizontal vertical method and of successive quadratic programming with a Hessian approximation exact on the tangent space of the constraints. One example shows that these methods in general are not one-step superlinearly convergent.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • P.T. Boggs, J.W. Tolle and P. Wang, “On the local convergence of quasi-Newton methods for constrained optimization”,SIAM Journal on Control and Optimization 20 (1982), 161–171.

    Google Scholar 

  • T.F. Coleman and A.R. Conn, “Nonlinear programming via an exact penalty function method: asymptotic analysis”,Mathematical Programming 24 (1982), 123–136.

    Google Scholar 

  • T.F. Coleman and A.R. Conn, “On the local convergence of a quasi-Newton method for a nonlinear programming problem”, Technical Report 82-509, Department of Computer Science, Cornell University (Ithaca, NY, 1982).

    Google Scholar 

  • R. Fontecilla, T. Steihaug and R. Tapia, “A convergence theory for a class of quasi-Newton methods for constrained optimization”, Technical Report 83-15, Department of Mathematical Sciences, Rice University (Houston, 1983).

    Google Scholar 

  • M.J.D. Powell, “The convergence of variable metric methods for nonlinearly constrained optimization calculations”, in: O. Mangasarian, R. Meyer and S. Robinson, eds.,Nonlinear Programming 3 (Academic Press, New York, 1978) pp. 27–63.

    Google Scholar 

  • Y. Yuan, “On the reduced Hessian method for constrained optimization”, Technical Report DAMTP 1984/NA1, Department of Applied Mathematics and Theoretical Physics, Cambridge University (Cambridge, England, 1984).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Colorado, 80309, Boulder, CO, USA

    Richard H. Byrd

Authors
  1. Richard H. Byrd
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was supported by National Science Foundation Grant MCS-8115475.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Byrd, R.H. An example of irregular convergence in some constrained optimization methods that use the projected hessian. Mathematical Programming 32, 232–237 (1985). https://doi.org/10.1007/BF01586093

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01586093

Key words

Search

Navigation