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On duality for mathematical programs with vanishing constraints

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Abstract

In this paper, we formulate and study Wolfe and Mond–Weir type dual models for a difficult class of optimization problems known as the mathematical programs with vanishing constraints. We establish the weak, strong, converse, restricted converse and strict converse duality results under the assumptions of convexity and strict convexity between the primal mathematical program with vanishing constraints and the corresponding Wolfe type dual. We also derive the weak, strong, converse, restricted converse and strict converse duality results between the primal mathematical program with vanishing constraints and the corresponding Mond–Weir type dual under the assumptions of pseudoconvex, strict pseudoconvex and quasiconvex functions.

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Acknowledgments

The authors are thankful to the anonymous referees of the paper for their valuable comments and useful suggestions which helped to improve the paper in its present form and the editor. Author Vinay Singh is thankful to National Board for Higher Mathematics (NBHM), Department of Atomic Energy (DAE), Government of India for the Financial support as a Post Doctoral Fellow during the preparation of this manuscript. The research of Vivek Laha was supported by the Council of Scientific and Industrial Research (CSIR), New Delhi, Ministry of Human Resources Development, Government of India through University Grant Commission (UGC) Research Fellowship Grant 20-06/2010 (i) EU-IV. Currently, Vivek Laha is supported by NBHM Postdoctoral Fellowship of Department of Atomic Energy, Government of India (Ref. No. 2/40(47)/2014/R & D-II/1170).

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Banaras Hindu University, Varanasi, 221 005, India

    S. K. Mishra & Vivek Laha

  2. Department of Mathematics, National Institute of Technology, Chaltlang, Aizawl, 796012, Mizoram, India

    Vinay Singh

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  1. S. K. Mishra
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Correspondence to Vivek Laha.

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Mishra, S.K., Singh, V. & Laha, V. On duality for mathematical programs with vanishing constraints. Ann Oper Res 243, 249–272 (2016). https://doi.org/10.1007/s10479-015-1814-8

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