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New dualities for mathematical programs with vanishing constraints

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  • Qingjie Hu

    (Guilin University of Electronic Technology)

  • Jiguang Wang

    (Guilin University of Electronic Technology)

  • Yu Chen

    (Guangxi Normal University)

Abstract

Recently, Mishra et al. (Ann Oper Res 243(1):249–272, 2016) formulate and study the Wolfe and the Mond–Weir type dual models for the mathematical programs with vanishing constraints. They establish the weak, strong, converse, restricted converse and strict converse duality results between the primal mathematical programs with vanishing constraints and the corresponding dual model under some assumptions. However, their models contain the calculation of the index sets, this makes it difficult to solve them from algorithm point of view. In this paper, we propose the new Wolfe and Mond–Weir type dual models for the mathematical programs with vanishing constraints, which do not involve the calculation of the index set. We show that the weak, strong, converse and restricted converse duality results hold between the primal mathematical programs with vanishing constraints and the corresponding new dual models under the same assumptions as the ones of Mishra et al.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:287:y:2020:i:1:d:10.1007_s10479-019-03409-6
    DOI: 10.1007/s10479-019-03409-6
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    References listed on IDEAS

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    1. Jin-Chirng Lee & Hang-Chin Lai, 2005. "Parameter-Free Dual Models for Fractional Programming with Generalized Invexity," Annals of Operations Research, Springer, vol. 133(1), pages 47-61, January.
    2. 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.
    3. S. Askar & A. Tiwari, 2009. "First-order optimality conditions and duality results for multi-objective optimisation problems," Annals of Operations Research, Springer, vol. 172(1), pages 277-289, November.
    4. Yogendra Pandey & Shashi Kant Mishra, 2016. "Duality for Nonsmooth Optimization Problems with Equilibrium Constraints, Using Convexificators," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 694-707, November.
    5. Matúš Benko & Helmut Gfrerer, 2017. "An SQP method for mathematical programs with vanishing constraints with strong convergence properties," Computational Optimization and Applications, Springer, vol. 67(2), pages 361-399, June.
    6. Hang-Chin Lai & Tone-Yau Huang, 2012. "Nondifferentiable minimax fractional programming in complex spaces with parametric duality," Journal of Global Optimization, Springer, vol. 53(2), pages 243-254, June.
    7. Elmor Peterson, 2001. "The Fundamental Relations between Geometric Programming Duality, Parametric Programming Duality, and Ordinary Lagrangian Duality," Annals of Operations Research, Springer, vol. 105(1), pages 109-153, July.
    8. 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.
    9. Radu Boţ & André Heinrich, 2014. "Regression tasks in machine learning via Fenchel duality," Annals of Operations Research, Springer, vol. 222(1), pages 197-211, November.
    10. 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.
    11. Altannar Chinchuluun & Dehui Yuan & Panos Pardalos, 2007. "Optimality conditions and duality for nondifferentiable multiobjective fractional programming with generalized convexity," Annals of Operations Research, Springer, vol. 154(1), pages 133-147, October.
    12. 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.
    13. T.R. Jefferson & C.H. Scott, 2001. "Quality Tolerancing and Conjugate Duality," Annals of Operations Research, Springer, vol. 105(1), pages 185-200, July.
    14. R.T. Rockafellar, 1999. "Duality and optimality in multistagestochastic programming," Annals of Operations Research, Springer, vol. 85(0), pages 1-19, January.
    15. Yogendra Pandey & S. K. Mishra, 2018. "Optimality conditions and duality for semi-infinite mathematical programming problems with equilibrium constraints, using convexificators," Annals of Operations Research, Springer, vol. 269(1), pages 549-564, October.
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    Cited by:

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