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Nonsmooth semi-infinite minmax programming involving generalized (Φ,ρ)-invexity

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Abstract

This paper introduces some new generalizations of the concept of (Φ,ρ)-invexity for nondifferentiable locally Lipschitz functions using the tools of Clarke subdifferential. These functions are used to derive the necessary and sufficient optimality conditions for a class of nonsmooth semi-infinite minmax programming problems, where set of restrictions are indexed in a compact set. Utilizing the sufficient optimality conditions, the authors formulate three types of dual models and establish weak and strong duality results. The results of the paper extend and unify naturally some earlier results from the literature.

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Authors and Affiliations

  1. Department of Basic Sciences & Humanities, National Institute of Technology, Takyelpat-795001, Imphal, Manipur, India

    B B Upadhyay & S K Mishra

Authors
  1. B B Upadhyay
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  2. S K Mishra
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Corresponding author

Correspondence to B B Upadhyay.

Additional information

The first author is supported by the National Board of Higher Mathematics (NBHM), Department of Atomic Energy, India, under Grant No. 2/40(12)/2014/R&D-II/10054.

This paper was recommended for publication by Editor WANG Shouyang.

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Upadhyay, B.B., Mishra, S.K. Nonsmooth semi-infinite minmax programming involving generalized (Φ,ρ)-invexity. J Syst Sci Complex 28, 857–875 (2015). https://doi.org/10.1007/s11424-015-2096-6

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  • DOI: https://doi.org/10.1007/s11424-015-2096-6

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