Skip to main content

Trust regions and projected gradients

  • Invited Lectures
  • Conference paper
  • First Online:
Book cover System Modelling and Optimization

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 113))

Work supported in part by the Applied Mathematical Sciences subprogram of the Office of Energy Research of the U.S. Department of Energy under Contract W-31-109-Eng-38.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Bertsekas, D. P. [1976]. On the Goldstein-Levitin-Polyak gradient projection method, IEEE Trans. Automat. Control 21, 174–184.

    Google Scholar 

  • Bertsekas, D. P. [1982]. Projected Newton methods for optimization problems with simple constraints, SIAM J. Control Optim. 20, 221–246.

    Google Scholar 

  • Burke, J. V. and J. J. Moré [1986]. On the identification of active constraints, Argonne National Laboratory, Mathematics and Computer Science Division Report ANL/MCS-TM-82, Argonne, Illinois.

    Google Scholar 

  • Calamai, P. H. and J. J. Moré [1987]. Projected gradient methods for linearly constrained problems, Mathematical Programming, 39, 93–116.

    Google Scholar 

  • Conn, A. R., Gould, N. I. M. and Ph. L. Toint [1986a]. Global convergence of a class of trust region algorithms for optimization problems with simple bounds, University of Namur, Department of Mathematics Report 86/1, Namur, Belgium.

    Google Scholar 

  • Conn, A. R., Gould, N. I. M. and Ph. L. Toint [1986b]. Testing a class of methods for solving minimization problems with simple bounds on the variables, University of Namur, Department of Mathematics Report 86/3, Namur, Belgium.

    Google Scholar 

  • Dunn, J. C. [1987a]. On the convergence of projected gradient processes to singular critical points, J. Optim. Theory Appl. 55, 203–216.

    Google Scholar 

  • Dunn, J. C. [1987b]. Projected Newton methods for nonlinearly constrained minimization problems, preprint.

    Google Scholar 

  • Gafni, E. M. and D. P. Bertsekas [1984]. Two-metric projection methods for constrained optimization, SIAM J. Control Optim. 22, 936–964

    Google Scholar 

  • Gawande, M. and J. C. Dunn [1987]. Variable metric gradient projection processes in convex feasible sets defined by nonlinear inequalities, preprint, to appear in J. Appl. Math. Optim.

    Google Scholar 

  • McCormick, G. P. and R. A. Tapia [1972]. The gradient projection method under mild differentiability conditions, SIAM J. Control 10, 93–98.

    Google Scholar 

  • Moré, J. J. [1983]. Recent developments in algorithms and software for trust region methods, in Mathematical Programming Bonn 1982 — The State of the Art, A. Bachem, M. Grötschel, B. Korte, eds., Springer-Verlag.

    Google Scholar 

  • Powell M. J. D. [1984]. On the global convergence of trust region algorithms for unconstrained minimization, Math. Programming 29, 297–303.

    Google Scholar 

  • Toint, Ph. L. [1987]. Global convergence of a class of trust region methods for nonconvex minimization in Hilbert space, University of Namur, Department of Mathematics Report 87/6, Namur, Belgium.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Masao Iri Keiji Yajima

Rights and permissions

Reprints and permissions

Copyright information

© 1988 International Federation for Information Processing

About this paper

Cite this paper

Moré, J.J. (1988). Trust regions and projected gradients. In: Iri, M., Yajima, K. (eds) System Modelling and Optimization. Lecture Notes in Control and Information Sciences, vol 113. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0042769

Download citation

  • DOI: https://doi.org/10.1007/BFb0042769

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19238-1

  • Online ISBN: 978-3-540-39164-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics