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On Semi-infinite Mathematical Programming Problems with Equilibrium Constraints Using Generalized Convexity

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Abstract

In this paper, we consider semi-infinite mathematical programming problems with equilibrium constraints (SIMPPEC). By using the notion of convexificators, we establish sufficient optimality conditions for the SIMPPEC. We formulate Wolfe and Mond–Weir-type dual models for the SIMPPEC under the invexity and generalized invexity assumptions. Weak and strong duality theorems are established to relate the SIMPPEC and two dual programs in the framework of convexificators.

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Acknowledgements

The authors are thankful to the anonymous referees for their valuable comments and suggestions which helped to improve the presentation of the paper.

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Authors and Affiliations

  1. Centre for Interdisciplinary Mathematical Sciences, Department of Science & Technology, Institute of Science, Banaras Hindu University, Varanasi, 221005, India

    Bhuwan Chandra Joshi

  2. Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, 221005, India

    Shashi Kant Mishra

  3. Mahila Maha Vidyalaya, Banaras Hindu University, Varanasi, 221005, India

    Pankaj Kumar

Authors
  1. Bhuwan Chandra Joshi
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  2. Shashi Kant Mishra
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  3. Pankaj Kumar
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Correspondence to Bhuwan Chandra Joshi.

Additional information

The research of Shashi Kant Mishra was supported by Department of Science and Technology-Science and Engineering Research Board (No. MTR/2018/000121), India.

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Joshi, B.C., Mishra, S.K. & Kumar, P. On Semi-infinite Mathematical Programming Problems with Equilibrium Constraints Using Generalized Convexity. J. Oper. Res. Soc. China 8, 619–636 (2020). https://doi.org/10.1007/s40305-019-00263-y

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  • DOI: https://doi.org/10.1007/s40305-019-00263-y

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