Skip to main content
SpringerLink
Log in

Characterizations of Variable Domination Structures via Nonlinear Scalarization

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

Abstract

In this paper, a nonlinear scalarization function is introduced for a variable domination structure. It is shown that this function is positively homogeneous, subadditive, and strictly monotone. This nonlinear function is then applied to characterize the weakly nondominated solution of multicriteria decision making problems and the solution of vector variational inequalities.

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. YU, P. L., Multiple-Criteria Decision Making: Concepts, Techniques, and Extensions, Plenum Press, New York, NY, 1985.

    Google Scholar 

  2. CHEN, G. Y., Existence of Solutions for a Vector Variational Inequality: An Extension of the Hartmann-Stampacchia Theorem, Journal of Optimization Theory and Applications, Vol. 74, pp. 445-456, 1992.

    Google Scholar 

  3. DANIILIDIS, A., and HADJISAVVAS, N., Existence Theorems for Vector Variational Inequalities, Bulletin of the Australian Mathematical Society, Vol. 54, pp. 473-481, 1996.

    Google Scholar 

  4. KONNO, I. V., and YAO, J. C., On the Generalized Vector Variational Inequality Problem, Journal of Mathematical Analysis and Applications, Vol 234, pp. 42-58, 1997.

    Google Scholar 

  5. OETTLI, W., and SCHLAGER, D., Existence of Equilibria for Monotone Multivalued Mappings, Mathematical Methods of Operations Research, Vol 48, pp. 219-228, 1998.

    Google Scholar 

  6. JAHN, J., Scalarization in Multiobjective Optimization, Mathematics of Multiobjective Optimization, Edited by P. Serafini, Springer Verlag, New York, NY, pp. 45-48, 1985.

    Google Scholar 

  7. TANINO, T., and SAWARAGI, Y., Stability of Nondominated Solutions in Multicriteria Decision Making, Journal of Optimization Theory and Applications, Vol. 30, pp. 229-253, 1980.

    Google Scholar 

  8. GERTH, C., and WEIDNER, P., Nonconvex Separation Theorems and Some Applications in Vector Optimization, Journal of Optimization Theory and Applications, Vol. 67, pp. 297-320, 1990.

    Google Scholar 

  9. CHEN, G. Y., GOH, C. J., and YANG, X. Q., Vector Network Equilibrium Problems and Nonlinear Scalarization Methods, Mathematical Methods of Operations Research, Vol. 49, pp. 239-253, 1999.

    Google Scholar 

  10. AUBIN, J. P., and EKELAND, I., Applied Nonlinear Analysis, Wiley, New York, NY, 1984.

    Google Scholar 

  11. GOH, C. J., and YANG, X. Q., On the Solution of a Vector Variational Inequality, Proceedings of 4th International Conference on Optimization Techniques and Applications, Edited by L. Caccetta et al, pp. 1548-1164, 1998.

Download references

Author information

Authors and Affiliations

  1. Chinese Academy of Sciences, Institute of Systems Science, Beijing, PRC

    G. Y. Chen (Professor)

  2. Department of Applied Mathematics, Hong Kong Polytechnic University, Kowloon, Hong Kong

    X. Q. Yang (Associate Professor)

Authors
  1. G. Y. Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. X. Q. Yang
    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

Chen, G.Y., Yang, X.Q. Characterizations of Variable Domination Structures via Nonlinear Scalarization. Journal of Optimization Theory and Applications 112, 97–110 (2002). https://doi.org/10.1023/A:1013044529035

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1013044529035

Search

Navigation