Skip to main content
SpringerLink
Log in

Scalarization and Nonlinear Scalar Duality for Vector Optimization with Preferences that are not necessarily a Pre-order Relation

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

Abstract

We consider problems of vector optimization with preferences that are not necessarily a pre-order relation. We introduce the class of functions which can serve for a scalarization of these problems and consider a scalar duality based on recently developed methods for non-linear penalization scalar problems with a single constraint.

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. Gasimov, R. (2001), Characterization of the Benson proper efficiency and scalarization in nonconvex vector optimization, In: Lecture Notes in Economic Mathematics Vol. 507, Springer, Berlin, pp. 189–198.

    Google Scholar 

  2. Henig, M. (1982), Proper efficiency withrespect to cones, Journal of Optimization Theory and Applications, 36, 387–407.

    Google Scholar 

  3. Huang, X.X. and Yang, X.Q. (2001), Duality and exact penalization for vector optimization via augmented Lagragian, Journal of Optimization Theory and Applications, 111, 615–640.

    Google Scholar 

  4. Huang, X.X and Yang, X.Q. Nonlinear Lagrangian for multiobjective optimization and applications to duality and exact penalization, submitted paper.

  5. Luc, D.T. (1989), Theory of Vector Optimization, Lecture Notes, Economic Mathematic Systems, Springer, Berlin.

    Google Scholar 

  6. Makarov, V.L., Levin, M.J. and Rubinov, A.M. (1995), Mathematical Economic Theory: Pure and Mixed Types of Economic Mechanisms, North-Holland, Amsterdam.

    Google Scholar 

  7. Rubinov, A.M. (1977), Sublinear operators and their applications, Uspehi Mat. Nauk (Russian Mathematical Survey), 32, 113–174.

    Google Scholar 

  8. Rubinov, A.M. (2000), Abstract Convexity and Global Optimization, Kluwer Academic Publishers, Dordrecht.

    Google Scholar 

  9. Rubinov, A.M. and Singer, I. (2001), Topical and sub-topical functions, downward sets and abstract convexity, Optimization, 50, 301–357.

    Google Scholar 

  10. Rubinov, A.M. and Yang, X.Q. Lagrange-type Functions in Constrained Non-convex Optimization, Kluwer Academic Publishers, Dordrecht, to appear.

  11. Sawaragi, Y. Nakayama, H. and Tanino, T. (1985), Theory of Multiobjective Optimization, Academic Press, New York.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. SITMS, University of Ballarat, Victoria, 3353, Australia (e-mail

    A.M. Rubinov & R.N. Gasimov

Authors
  1. A.M. Rubinov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R.N. Gasimov
    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., Gasimov, R. Scalarization and Nonlinear Scalar Duality for Vector Optimization with Preferences that are not necessarily a Pre-order Relation. Journal of Global Optimization 29, 455–477 (2004). https://doi.org/10.1023/B:JOGO.0000047914.22567.66

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:JOGO.0000047914.22567.66

Search

Navigation