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Approximations for Pareto and Proper Pareto solutions and their KKT conditions

Author

Listed:
  • P. Kesarwani

    (Indian Institute of Technology)

  • P. K. Shukla

    (Alliance Manchester Business School
    Institute AIFB, Karlsruhe Institute of Technology)

  • J. Dutta

    (Indian Institute of Technology)

  • K. Deb

    (Michigan State University)

Abstract

In this article, we view the Pareto and weak Pareto solutions of the multiobjective optimization by using an approximate version of KKT type conditions. In one of our main results Ekeland’s variational principle for vector-valued maps plays a key role. We also focus on an improved version of Geoffrion proper Pareto solutions and it’s approximation and characterize them through saddle point and KKT type conditions.

Suggested Citation

  • P. Kesarwani & P. K. Shukla & J. Dutta & K. Deb, 2022. "Approximations for Pareto and Proper Pareto solutions and their KKT conditions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(1), pages 123-148, August.
    • Handle: RePEc:spr:mathme:v:96:y:2022:i:1:d:10.1007_s00186-022-00787-9
    DOI: 10.1007/s00186-022-00787-9
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    References listed on IDEAS

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    1. Gabriele Eichfelder & Leo Warnow, 2021. "Proximity measures based on KKT points for constrained multi-objective optimization," Journal of Global Optimization, Springer, vol. 80(1), pages 63-86, May.
    2. Joydeep Dutta & Kalyanmoy Deb & Rupesh Tulshyan & Ramnik Arora, 2013. "Approximate KKT points and a proximity measure for termination," Journal of Global Optimization, Springer, vol. 56(4), pages 1463-1499, August.
    3. Hiroki Tanabe & Ellen H. Fukuda & Nobuo Yamashita, 2019. "Proximal gradient methods for multiobjective optimization and their applications," Computational Optimization and Applications, Springer, vol. 72(2), pages 339-361, March.
    4. G. Cocchi & G. Liuzzi & S. Lucidi & M. Sciandrone, 2020. "On the convergence of steepest descent methods for multiobjective optimization," Computational Optimization and Applications, Springer, vol. 77(1), pages 1-27, September.
    5. Giorgio Giorgi & Bienvenido Jiménez & Vicente Novo, 2016. "Approximate Karush–Kuhn–Tucker Condition in Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 70-89, October.
    6. Bennet Gebken & Sebastian Peitz, 2021. "An Efficient Descent Method for Locally Lipschitz Multiobjective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 188(3), pages 696-723, March.
    7. C. Gutiérrez & B. Jiménez & V. Novo, 2006. "On Approximate Efficiency in Multiobjective Programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(1), pages 165-185, August.
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    Cited by:

    1. Braun, Marlon & Shukla, Pradyumn, 2024. "On cone-based decompositions of proper Pareto-optimality in multi-objective optimization," European Journal of Operational Research, Elsevier, vol. 317(2), pages 592-602.

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