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Symmetric Duality for Homogeneous Multiple-Objective Problems

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Abstract

In this article, we present a symmetric duality for a multiple-objective problem, which appears in the application of minimizing cost under a given demand constraint. The duality is constructed according to the quasi-conjugacy approach (Thach in SIAM J. Optim. 4:44–64, 1994) applied to nondecreasing homogeneous cost functions. By this duality approach, we obtain a duality equation that helps to characterize the (weakly) efficient solutions of the primal problem and the dual.

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References

  1. Thach, P.T.: A nonconvex duality with zero gap and applications. SIAM J. Optim. 4, 44–64 (1994)

    Article  MathSciNet  Google Scholar 

  2. Bitran, G.R.: Duality for nonlinear multiple-criteria optimization problems. J. Optim. Theory Appl. 35, 367–401 (1981)

    Article  MathSciNet  Google Scholar 

  3. Fandel, G., Gal, T. (eds.): Multiple Criteria Decisions Making Theory and Applications. Springer, New York (1984)

    MATH  Google Scholar 

  4. Sawaragi, Y., Nakayama, H., Tanino, T.: Theory of Multiobjective Optimization. Academic Press, Orlando (1985)

    MATH  Google Scholar 

  5. Yu, P.L.: Multiple-Criteria Decision Making. Plenum, New York (1985)

    Book  Google Scholar 

  6. Li, Z.M., Zhan, M.H.: Optimality conditions and Lagrange duality for vector extremum problems with set constraint. J. Optim. Theory Appl. 135, 323–352 (2007)

    Article  MathSciNet  Google Scholar 

  7. Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)

    Book  Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Hanoi, Vietnam

    Phan Thien Thach

Authors
  1. Phan Thien Thach
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Correspondence to Phan Thien Thach.

Additional information

Communicated by Harold P. Benson.

The author would like to thank anonymous referees for helpful comments and suggestions to revise the article.

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Thach, P.T. Symmetric Duality for Homogeneous Multiple-Objective Problems. J Optim Theory Appl 188, 317–331 (2021). https://doi.org/10.1007/s10957-011-9822-6

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  • DOI: https://doi.org/10.1007/s10957-011-9822-6

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