Skip to main content
SpringerLink
Log in

On Global Optimality Conditions via Separation Functions

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

Abstract

The paper examines some axiomatic definitions of separation functions that can be employed fruitfully in the analysis of side-constrained extremum problems. A study of their general properties points out connections with abstract convex analysis and recent generalizations of Lagrangian approaches to duality and exact penalty methods. Many concrete examples are brought out.

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

Access this article

Log in via an institution

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

  1. Giannessi, F., Theorems of the Alternative and Optimality Conditions, Journal of Optimization Theory and Applications, Vol. 42, pp. 331–365, 1984.

    Google Scholar 

  2. Giannessi, F., and RapcsÁk, T., Images, Separation of Sets, and Extremum Problems, Recent Trends in Optimization Theory and Applications, Edited by R. P. Agarwal, World Scientific, Singapore, Republic of Singapore, pp. 79–106, 1995.

    Google Scholar 

  3. Giannessi, F., Separation of Sets and Gap Functions for Quasi-Variational Inequalities, Variational Inequalities and Network Equilibrium Problems, Edited by F. Giannessi and A. Maugeri, Plenum Press, New York, NY, pp. 101–121, 1996.

    Google Scholar 

  4. Giannessi, F., On Connections among Separation, Penalization, and Regularization for Variational Inequalities with Point-to-Set Operators, Proceedings of the Workshop on Equilibrium Problems with Side Constraints: Lagrangian Theory and Duality, Supplementi ai Rendiconti del Circolo Matematico di Palermo, Serie II, No. 48, pp. 137–145, 1997.

  5. Singer, I., Abstract Convex Analysis, Wiley and Sons, New York, NY, 1997.

    Google Scholar 

  6. Pallaschke, D., and Rolewicz, S., Foundations of Mathematical Optimization, Kluwer Academic Publishers, Dordrecht, Holland, 1997.

    Google Scholar 

  7. Rubinov, A., Abstract Convexity and Global Optimization, Kluwer Academic Publishers, Dordrecht, Holland, 2000.

    Google Scholar 

  8. Pappalardo, M., Image Space Approach to Penalty Methods, Journal of Optimization Theory and Applications, Vol. 64, pp. 141–152, 1990.

    Google Scholar 

  9. Rubinov, A., Glover, B. M., and Yang, X. Q., Extended Lagrange and Penalty Functions in Continuous Optimization, Optimization, Vol. 46, pp. 327–351, 1999.

    Google Scholar 

  10. Rubinov, A., Glover, B. M., and Yang, X. Q. Decreasing Functions with Applications to Optimization, SIAM Journal on Optimization, Vol. 10, pp. 289–313, 2000.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Information Technology and Mathematical Sciences, University of Ballarat, Victoria, Australia

    A. M. RUBINOV (Professor)

  2. Faculty of Economics, University of Trieste, Trieste, Italy

    A. UDERZO (PhD Fellow)

Authors
  1. A. M. RUBINOV
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. UDERZO
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

RUBINOV, A.M., UDERZO, A. On Global Optimality Conditions via Separation Functions. Journal of Optimization Theory and Applications 109, 345–370 (2001). https://doi.org/10.1023/A:1017566406216

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1017566406216

Search

Navigation