Skip to main content

Lower Semicontinuity of Marginal Functions

  • Conference paper

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 226))

Abstract

Criteria for the lower semicontinuity of marginal functions constitute one of the most important topics of optimization.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Attouch, H., Wets, R., Approximation and convergence in nonlinear optimization, in NONLINEAR PROGRAMMING 4, O. Mangasarian, R. Meyer, S. Robinsons (editors), Acad. Press, New York 1981, 367–394.

    Google Scholar 

  2. Bank, B, Guddat, J., Klatte, D., Kummer B., Tammer, K., NON LINEAR PARAMETRIC OPTIMIZATION, Akademie Verlag, Berlin 1982.

    Google Scholar 

  3. Berge, C., TOPOLOGICAL SPACES, Mc Millan Co., New York, 1963.

    Google Scholar 

  4. De Giorgi, E., Franzoni, T., Su un tipo di convergenza variazionale, ATTI ACCAD. NAZ. LINCEI, SCIENZE FIS. MAT. NAT., 58 (1975), 842–850.

    Google Scholar 

  5. Dolecki, S., Abstract study of optimality conditions, J. Math. Anal. Appl., 73 (1980), 24–48.

    Article  Google Scholar 

  6. Dolecki, S., Corrigendum 82 (1981), 295–296.

    Google Scholar 

  7. Dolecki, S., Bounded controlling sequences, lower stability and certain penalty procedures, Appl. Math. Optimization, 4 (1977), 15–26.

    Article  Google Scholar 

  8. Dolecki, S., Constraints stability and moduli of semicontinuity, unpublished (1977).

    Google Scholar 

  9. Dolecki, S., Convergence of global minima and infima, Math. Operationsforsch. Stat. Optimization, to appear.

    Google Scholar 

  10. Dolecki, S., Greco, G.H., Lechicki, A., Compactoid and compact filters, Pacific J. Math., to appear.

    Google Scholar 

  11. Dolecki, S., Lechicki, A., On structure of upper semicontinuity, J. Math. Anal. Appl. 88 (1982), 547–554).

    Article  Google Scholar 

  12. Dolecki, S., Rolewicz, S., A characterization of semicontinuity-preserving multifunctions, J. Math. Anal. Appl. 65 (1978), 26–31.

    Article  Google Scholar 

  13. Dolecki, S., Rolewicz, S., Metric characterizations of upper semicontinuity, J. Math. Anal. Appl. 69 (1979), 146–152.

    Article  Google Scholar 

  14. Hiriart-Urruty, J.-B., Gradients généralisés de fonctions marginales, SIAM J. Control Optim. 16 (1978), 301–316.

    Article  Google Scholar 

  15. Kurcyusz, S., Some remarks on generalized Lagrangians, Proc. 7th IFIP Conference, Nice, September 1975, Sptinger Verlag 1976.

    Google Scholar 

  16. Laurent, F.J., APPROXIMATION AT OPTIMAZATION, Hermann, Paris 1972.

    Google Scholar 

  17. Lechicki, A., Ziemińska, J., Closed filters and graph-closed multi-functions in convergence spaces, to appear.

    Google Scholar 

  18. Lucchetti, R., On the continuity of the optimal value and of the optimal set in minimum problems, to appear.

    Google Scholar 

  19. Penot, J.-P., Continuity properties of performance functions, in OPTIMIZATION THEORY AND ALGORITHMS, J.-B. Hiriart-Urruty, W. Oettli, J. Stoer (editors), M. Dekker, New York 1983.

    Google Scholar 

  20. Rockafellar, R.T., Lagrange multipliers and subderivatives in nonlinear programming, Math. Programming Study, 17 (1982), 28–66.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dolecki, S. (1984). Lower Semicontinuity of Marginal Functions. In: Hammer, G., Pallaschke, D. (eds) Selected Topics in Operations Research and Mathematical Economics. Lecture Notes in Economics and Mathematical Systems, vol 226. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45567-4_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-45567-4_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12918-9

  • Online ISBN: 978-3-642-45567-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics