Skip to main content
SpringerLink
Log in

A New Approach to a Multicriteria Optimization Problem

  • Published:
Numerical Algorithms Aims and scope Submit manuscript

Abstract

We present a new approach to a multicriteria optimization problem, where the objective and the constraints are linear functions. From an equivalent equilibrium problem, first suggested in [5,6,8], we show new characterizations of weakly efficient points based on the partial order induced by a nonempty closed convex cone in a finite-dimensional linear space, as in [7]. Thus, we are able to apply the analytic center cutting plane algorithm that finds equilibrium points approximately, by Raupp and Sosa [10], in order to find approximate weakly efficient solutions of MOP.

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. I. Das and J.E. Dennis, Normal-boundary intersection: a new method for generating the Pareto surface in nonlinear optimization problems, SIAM J. Optim. 8 (1998) 631–657.

    Google Scholar 

  2. J.-L. Goffin, J. Gonzio, R. Sarkissian and J.-P. Vial, Solving nonlinear multicommodity flow problems by analytic center cutting plane method, Math. Programming Ser. B 76(1), Interior Point Methods in Theory and Practice, ed. K.M. Anstreicher (1997) 131–154.

  3. J.-L. Goffin, Z.Q. Luo and Y. Ye, Complexity analysis of an interior cutting plane method for convex feasibility problems, SIAM J. Optim. 6 (1996) 638–652.

    Google Scholar 

  4. L.M. Graña Drummond, A.N. Iusem and B.F. Svaiter, First order optimality conditions for Pareto optimization of vector-valued functions, Technical Report IMPA (February 2000).

  5. A.N. Iusem and W. Sosa, Iterative algorithms for equilibrium problem, Optimization 52 (2003) 301–316.

    Google Scholar 

  6. A.N. Iusem and W. Sosa, New existence results for equilibrium problem, Nonlinear Anal. Theory Methods Appl. 52 (2003) 621–635.

    Google Scholar 

  7. D.T. Luc, Theory of Vector Optimization, Lecture Notes in Economics and Mathematical Systems, Vol. 319 (Springer, Berlin, 1989).

    Google Scholar 

  8. W. Oettli, A remark on vector-valued equilibria and generalized monotonicity, Acta Math. Vietnamita 22 (1997).

  9. F.M.P. Raupp and C.C. Gonzaga, A center cutting plane algorithm for a likelihood estimate problem, Comput. Optim Appl. 21 (2001).

  10. F.M.P. Raupp and W. Sosa, An analytic center cutting plane algorithm for finding equilibrium points, Technical Report LNCC (April 2000).

  11. P. Ruiz-Canales and A. Rufián-Lizana, A characterization of weakly efficient points, Math. Programming (1994).

  12. R.B. Statnikov and J.B. Matusov, Multicriteria Optimization and Engineering (Chapman and Hall, New York, 1995).

    Google Scholar 

  13. Y. Ye, Interior Point Algorithms, Theory and Analysis, Wiley-Interscience Series in Discrete Mathematics and Optimization (Wiley, New York, 1997).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Instituto de Matemática e Ciencias Afines, Universidad Nacional de Ingenieria, Peru

    Wilfredo Sosa

  2. Laboratório Nacional de Computação Científica, MCT, Brazil

    Fernanda M.P. Raupp

Authors
  1. Wilfredo Sosa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fernanda M.P. Raupp
    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

Sosa, W., Raupp, F.M. A New Approach to a Multicriteria Optimization Problem. Numerical Algorithms 35, 233–247 (2004). https://doi.org/10.1023/B:NUMA.0000021770.77789.b7

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:NUMA.0000021770.77789.b7

Search

Navigation