Skip to main content
SpringerLink
Log in
Book cover

IFIP Technical Conference on Optimization Techniques

Optimization Techniques 1973: 5th Conference on Optimization Techniques Part I pp 418–425Cite as

Penalty methods and augmented Lagrangians in nonlinear programming

  • Mathematical Programming
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3))

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. K. J. Arrow, F. J. Gould and S. M. Howe, "A general saddle point result for constrained optimization", Institute of Statistics Mimeo Series No. 774, Univ. of N. Carolina (Chapel Hill), 1971.

    Google Scholar 

  2. K. J. Arrow and R. M. Solow, "Gradient methods for constrained maxima, with weakened assumptions", in Studies in Linear and Nonlinear Programming, K. Arrow, L. Hurwicz and H. Uzawa (editors), Stanford Univ. Press, 1958.

    Google Scholar 

  3. D. P. Bertsekas, "Combined primal-dual and penalty methods for constrained minimization", SIAM J. Control, to appear.

    Google Scholar 

  4. J. D. Buys, "Dual algorithms for constrained optimization", Thesis, Leiden, 1972.

    Google Scholar 

  5. A. V. Fiacco and G. P. McCormick, Nonlinear Programming: Sequential Unconstrained Optimization Techniques, Wiley, 1968.

    Google Scholar 

  6. R. Fletcher, "A class of methods for nonlinear programming with termination and convergence properties", in Integer and Nonlinear Programming, J. Abadie (editor), North-Holland, 1970.

    Google Scholar 

  7. R. Fletcher, "A class of methods for non-linear programming III: Rates of convergence", in Numerical Methods for Non-linear Optimization, F. A. Lootsma (editor), Academic Press, 1973.

    Google Scholar 

  8. R. Fletcher and S. Lill, "A class of methods for nonlinear programming, II: computational experience", in Nonlinear Programming, J. B. Rosen, O. L. Mangasarian and K. Ritter (editors), Academic Press, 1971.

    Google Scholar 

  9. P. C. Haarhoff and J. D. Buys, "A new method for the optimization of a nonlinear function subject to nonlinear constraints", Computer J. 13 (1970), 178–184.

    Article  Google Scholar 

  10. M. R. Hestenes, "Multiplier and gradient methods", J. Opt. Theory Appl. 4 (1969), 303–320.

    Article  Google Scholar 

  11. B. W. Kort and D. P. Bertsekas, "A new penalty function method for constrained minimization", Proc. of IEEE Decision and Control Conference, New Orleans, Dec. 1972.

    Google Scholar 

  12. S. A. Lill, "Generalization of an exact method for solving equality constrained problems to deal with inequality constraints", in Numerical Methods for Nonlinear Optimization, F. A. Lootsma (editor), Academic Press, 1973.

    Google Scholar 

  13. D. G. Luenberger, Introduction to linear and nonlinear programming, Addison-Wesley, 1973, 320–322.

    Google Scholar 

  14. O. L. Mangasarian, "Unconstrained Lagrangians in nonlinear programming", Computer Sciences Tech. Report #174, Univ. of Wisconsin, Madison, 1973.

    Google Scholar 

  15. A. Miele, E. E. Cragg, R. R. Iver and A. V. Levy, "Use of the augmented penalty function in mathematical programming, part I", J. Opt. Theory Appl. 8 (1971), 115–130.

    Article  Google Scholar 

  16. A. Miele, E. E. Cragg and A. V. Levy, "Use of the augmented penalty function in mathematical programming problems, part II", J. Opt. Theory Appl. 8 (1971, 131–153.

    Article  Google Scholar 

  17. A. Miele, P. E. Moseley and E. E. Cragg, "A modification of the method of multipliers for mathematical programming problems", in Techniques of Optimization, A. V. Balakrishnan (editor), Academic Press, 1972.

    Google Scholar 

  18. A. Miele, P. E. Moseley, A. V. Levy and G. M. Coggins, "On the method of multipliers for mathematical programming problems", J. Opt. Theory Appl. 10 (1972), 1–33.

    Article  Google Scholar 

  19. M. J. D. Powell, "A method for nonlinear optimization in minimization problems", in Optimization, R. Fletcher (editor), Academic Press, 1969.

    Google Scholar 

  20. R. T. Rockafellar, "New applications of duality in convex programming", written version of talk at 7th International Symposium on Math. Programming (the Hague, 1970) and elsewhere, published in the Proc. of the 4th Conference on Probability (Brasov, Romania, 1971).

    Google Scholar 

  21. R. T. Rockafellar, "A dual approach to solving nonlinear programming problems by unconstrained optimization", Math. Prog., to appear.

    Google Scholar 

  22. R. T. Rockafellar, "The multiplier method of Hestenes and Powell applied to convex programming", J. Opt. Theory Appl., to appear.

    Google Scholar 

  23. R. T. Rockafellar, "Augmented Lagrange multiplier functions and duality in nonconvex programming", SIAM J. Control, to appear.

    Google Scholar 

  24. R. D. Rupp, "A method for solving a quadratic optimal control problem", J. Opt. Theory Appl. 9 (1972), 238–250.

    Article  Google Scholar 

  25. R. D. Rupp, "Approximation of the classical isoperimetric problem", J. Opt. Theory Appl. 9 (1972), 251–264.

    Article  Google Scholar 

  26. S. S. Tripathi and K. S. Narendra, "Constrained optimization problems using multiplier methods", J. Opt. Theory Appl. 9 (1972), 59–70.

    Article  Google Scholar 

  27. A. P. Wierzbicki, "Convergence properties of a penalty shifting algorithm for nonlinear programming porblems with inequality constraints", Archiwum Automatiki i Telemechaniki (1970).

    Google Scholar 

  28. A. P. Wierzbicki, "A penalty function shifting method in constrained static optimization and its convergence properties", Archiwum Automatyki i Telemechaniki 16 (1971), 395–416.

    Google Scholar 

  29. A. P. Wierzbicki and A. Hatko, "Computational methods in Hilbert space for optimal control problems with delays", these proceedings.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Mathematics, University of Washington, 98195, Seattle, Washington, USA

    R. Tyrrell Rockafellar

Authors
  1. R. Tyrrell Rockafellar
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

R. Conti A. Ruberti

Rights and permissions

Reprints and permissions

Copyright information

© 1973 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Rockafellar, R.T. (1973). Penalty methods and augmented Lagrangians in nonlinear programming. In: Conti, R., Ruberti, A. (eds) 5th Conference on Optimization Techniques Part I. Optimization Techniques 1973. Lecture Notes in Computer Science, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-06583-0_41

Download citation

  • DOI: https://doi.org/10.1007/3-540-06583-0_41

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06583-8

  • Online ISBN: 978-3-540-37903-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation