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On directionally differentiable multiobjective programming problems with vanishing constraints

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  • Tadeusz Antczak

    (University of Lodz)

Abstract

In this paper, a class of directionally differentiable multiobjective programming problems with inequality, equality and vanishing constraints is considered. Under both the Abadie constraint qualification and the modified Abadie constraint qualification, the Karush–Kuhn–Tucker type necessary optimality conditions are established for such nondifferentiable vector optimization problems by using the nonlinear version Gordan theorem of the alternative for convex functions. Further, the sufficient optimality conditions for such directionally differentiable multiobjective programming problems with vanishing constraints are proved under convexity hypotheses. Furthermore, vector Wolfe dual problem is defined for the considered directionally differentiable multiobjective programming problem vanishing constraints and several duality theorems are established also under appropriate convexity hypotheses.

Suggested Citation

  • Tadeusz Antczak, 2023. "On directionally differentiable multiobjective programming problems with vanishing constraints," Annals of Operations Research, Springer, vol. 328(2), pages 1181-1212, September.
    • Handle: RePEc:spr:annopr:v:328:y:2023:i:2:d:10.1007_s10479-023-05368-5
    DOI: 10.1007/s10479-023-05368-5
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    References listed on IDEAS

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    1. Slimani, Hachem & Radjef, Mohammed Said, 2010. "Nondifferentiable multiobjective programming under generalized dI-invexity," European Journal of Operational Research, Elsevier, vol. 202(1), pages 32-41, April.
    2. Qingjie Hu & Jiguang Wang & Yu Chen, 2020. "New dualities for mathematical programs with vanishing constraints," Annals of Operations Research, Springer, vol. 287(1), pages 233-255, April.
    3. Wolfgang Achtziger & Tim Hoheisel & Christian Kanzow, 2013. "A smoothing-regularization approach to mathematical programs with vanishing constraints," Computational Optimization and Applications, Springer, vol. 55(3), pages 733-767, July.
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    5. S. K. Mishra & Vinay Singh & Vivek Laha, 2016. "On duality for mathematical programs with vanishing constraints," Annals of Operations Research, Springer, vol. 243(1), pages 249-272, August.
    6. Qingjie Hu & Yu Chen & Zhibin Zhu & Bishan Zhang, 2014. "Notes on Convergence Properties for a Smoothing-Regularization Approach to Mathematical Programs with Vanishing Constraints," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, September.
    7. A. F. Izmailov & M. V. Solodov, 2009. "Mathematical Programs with Vanishing Constraints: Optimality Conditions, Sensitivity, and a Relaxation Method," Journal of Optimization Theory and Applications, Springer, vol. 142(3), pages 501-532, September.
    8. Dominik Dorsch & Vladimir Shikhman & Oliver Stein, 2012. "Mathematical programs with vanishing constraints: critical point theory," Journal of Global Optimization, Springer, vol. 52(3), pages 591-605, March.
    9. Tadeusz Antczak, 2022. "Optimality conditions and Mond–Weir duality for a class of differentiable semi-infinite multiobjective programming problems with vanishing constraints," 4OR, Springer, vol. 20(3), pages 417-442, September.
    10. Antczak, Tadeusz, 2002. "Multiobjective programming under d-invexity," European Journal of Operational Research, Elsevier, vol. 137(1), pages 28-36, February.
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