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New dualities for mathematical programs with vanishing constraints

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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.

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Authors and Affiliations

  1. Guangxi Key Laboratory of Automatic Detecting Technology and Instruments, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, 541004, People’s Republic of China

    Qingjie Hu & Jiguang Wang

  2. School of Mathematics and Statistics, Guangxi Normal University, Guilin, 541004, People’s Republic of China

    Yu Chen

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  1. Qingjie Hu
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  2. Jiguang Wang
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  3. Yu Chen
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Correspondence to Qingjie Hu.

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This work is supported by National Natural Science Foundation of China (No. 11461015, 11961011, 11761014) of China, Guangxi Natural Science Foundation (No. 2015GXNSFAA139010, 2016GXNSFFA380009, 2017GXNSFAA198243) and Guangxi Key Laboratory of Automatic Detecting Technology (No.YQ17117).

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Hu, Q., Wang, J. & Chen, Y. New dualities for mathematical programs with vanishing constraints. Ann Oper Res 287, 233–255 (2020). https://doi.org/10.1007/s10479-019-03409-6

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