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Lagrange Multiplier Rules for Weakly Minimal Solutions of Compact-Valued Set Optimization Problems

Author

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  • Tijani Amahroq

    (Cadi Ayyad University, Faculty of Sciences and Techniques, B.P. 549, Marrakech, Morocco)

  • Abdessamad Oussarhan

    (Cadi Ayyad University, Faculty of Sciences and Techniques, B.P. 549, Marrakech, Morocco)

Abstract

Optimality conditions are established in terms of Lagrange–Fritz–John multipliers as well as Lagrange–Kuhn–Tucker multipliers for set optimization problems (without any convexity assumption) by using new scalarization techniques. Additionally, we indicate how these results may be applied to some particular weak vector equilibrium problems.

Suggested Citation

  • Tijani Amahroq & Abdessamad Oussarhan, 2019. "Lagrange Multiplier Rules for Weakly Minimal Solutions of Compact-Valued Set Optimization Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(04), pages 1-22, August.
    • Handle: RePEc:wsi:apjorx:v:36:y:2019:i:04:n:s0217595919500210
    DOI: 10.1142/S0217595919500210
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    References listed on IDEAS

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    1. Frank Heyde & Andreas Löhne & Christiane Tammer, 2009. "Set-valued duality theory for multiple objective linear programs and application to mathematical finance," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 159-179, March.
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    Cited by:

    1. Gemayqzel Bouza & Ernest Quintana & Christiane Tammer, 2021. "A Steepest Descent Method for Set Optimization Problems with Set-Valued Mappings of Finite Cardinality," Journal of Optimization Theory and Applications, Springer, vol. 190(3), pages 711-743, September.

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