Skip to main content
Log in

Convergence of bounds in optimization

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

Consider a sequence of extensionsI n of a real-valued functionI. Sufficient conditions for the convergence of the infimum ofI n to the infimum ofI are obtained. These conditions are applied to an eigenvalue problem.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Fichera, G.,Linear Elliptic Differential Systems and Eigenvalue Problems, Springer-Verlag, Berlin, Germany, 1965.

    MATH  Google Scholar 

  2. Gould, S. H.,Variational Methods for Eigenvalue Problems, University of Toronto Press, Toronto, Canada, 1957.

    MATH  Google Scholar 

  3. Krotov, V. F.,Approximate Synthesis of Optimal Controls, Automation and Remote Control, Vol. 25, No. 11, 1964.

  4. Rozenberg, G. S.,Analytical Estimation of the Degree of Optimality of Controlled Systems, Automation and Remote Control, Vol. 27, No. 10, 1966.

  5. Stoddart, A. W. J.,Estimation of Optimality for Multidimensional Control Systems, Journal of Optimization Theory and Applications, Vol. 3, No. 6, 1969.

  6. Stoddart, A. W. J.,Semicontinuity of Integrals, Transactions of the American Mathematical Society, Vol. 122, No. 1, 1966.

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by M. R. Hestenes

This work was supported in part by the National Science Foundation under Grant No. GP-14595.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Stoddart, A.W.J. Convergence of bounds in optimization. J Optim Theory Appl 12, 563–566 (1973). https://doi.org/10.1007/BF00934778

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00934778

Keywords

Navigation