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Optimality Conditions for Vector Optimization Problems with Difference of Convex Maps

Author

Listed:
  • X. L. Guo

    (Chongqing University
    Henan Institute of Engineering)

  • S. J. Li

    (Chongqing University)

Abstract

In this paper, by using the notion of strong subdifferential and epsilon-subdifferential, necessary optimality conditions are established firstly for an epsilon-weak Pareto minimal point and an epsilon-proper Pareto minimal point of a vector optimization problem, where its objective function and constraint set are denoted by using differences of two vector-valued maps, respectively. Then, by using the concept of approximate pseudo-dissipativity, sufficient optimality conditions are obtained. As an application of these results, sufficient and necessary optimality conditions are also given for an epsilon-weak Pareto minimal point and an epsilon-proper Pareto minimal point of a vector fractional mathematical programming.

Suggested Citation

  • X. L. Guo & S. J. Li, 2014. "Optimality Conditions for Vector Optimization Problems with Difference of Convex Maps," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 821-844, September.
    • Handle: RePEc:spr:joptap:v:162:y:2014:i:3:d:10.1007_s10957-013-0327-3
    DOI: 10.1007/s10957-013-0327-3
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    References listed on IDEAS

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    1. S. J. Li & S. K. Zhu & X. B. Li, 2012. "Second-Order Optimality Conditions for Strict Efficiency of Constrained Set-Valued Optimization," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 534-557, November.
    2. Guang Ya Chen & Johannes Jahn, 1998. "Optimality conditions for set-valued optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(2), pages 187-200, November.
    3. Radu Boţ & Delia-Maria Nechita, 2011. "On the Dini-Hadamard subdifferential of the difference of two functions," Journal of Global Optimization, Springer, vol. 50(3), pages 485-502, July.
    4. J. Baier & J. Jahn, 1999. "On Subdifferentials of Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 100(1), pages 233-240, January.
    5. Jean-Paul Penot, 2011. "The directional subdifferential of the difference of two convex functions," Journal of Global Optimization, Springer, vol. 49(3), pages 505-519, March.
    6. F. Flores-BAZÁN & W. Oettli, 2001. "Simplified Optimality Conditions for Minimizing the Difference of Vector-Valued Functions," Journal of Optimization Theory and Applications, Springer, vol. 108(3), pages 571-586, March.
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    Cited by:

    1. Yldenilson Torres Almeida & João Xavier Cruz Neto & Paulo Roberto Oliveira & João Carlos de Oliveira Souza, 2020. "A modified proximal point method for DC functions on Hadamard manifolds," Computational Optimization and Applications, Springer, vol. 76(3), pages 649-673, July.
    2. Allahkaram Shafie & Farid Bozorgnia, 2019. "A Note on the Paper “Optimality Conditions for Vector Optimization Problems with Difference of Convex Maps”," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 837-849, August.
    3. Glaydston Carvalho Bento & Sandro Dimy Barbosa Bitar & João Xavier Cruz Neto & Antoine Soubeyran & João Carlos Oliveira Souza, 2020. "A proximal point method for difference of convex functions in multi-objective optimization with application to group dynamic problems," Computational Optimization and Applications, Springer, vol. 75(1), pages 263-290, January.

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