Skip to main content

Theorems of the alternative and their applications in multiobjective optimization

This is a preview of subscription content, access via your institution.


  1. M. Avriel,Nonlinear programming, Prentice Hall, (New Jersey, 1976).

    Google Scholar 

  2. R. T. Rockafellar,Convex analysis, Princeton University Press (1970).

  3. J. M. Borwein, The geometry of Pareto efficiency over cones,Math. Oper. Statist., Ser. Optimization,11 (1980), 235–248.

    Google Scholar 

  4. R. Lehmann, W. Oettli, The theorem of the alternative, the key theorem and the vector maximization problem,Math. Programming,8 (1975), 332–344.

    Article  Google Scholar 

  5. S. Smale, Global analysis and economics V,J. Math. Econ.,1 (1974), 213–221.

    Article  Google Scholar 

  6. D. T. Luc, On duality in multiobjective programming,J. Optimization Theory Appl.,43 (1984), 557–582.

    Article  Google Scholar 

  7. D. T. Luc,Contributions to the duality theory in mathematical programming, Ph. D. Thesis (Budapest, 1983).

Download references

Author information

Authors and Affiliations


Rights and permissions

Reprints and Permissions

About this article

Cite this article

Luc, D.T. Theorems of the alternative and their applications in multiobjective optimization. Acta Math Hung 45, 311–320 (1985).

Download citation

  • Received:

  • Issue Date:

  • DOI: