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Optimality conditions for semi-infinite programming problems involving generalized convexity

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Abstract

We apply some advanced tools of quasiconvex analysis to establish Karush–Kuhn–Tucker type necessary and sufficient optimality conditions for non-differentiable semi-infinite programming problems. In addition, we propose a linear characterization of optimality for the mentioned problems. Examples are also designed to analyze and illustrate the results obtained.

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Acknowledgements

The authors are grateful to professor Miguel Ángel Goberna for his many helpful suggestions which have improved the presentation of the paper. Also, we would like to thank the three anonymous referees for carefully reading our work and for their helpful comments.

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Authors and Affiliations

  1. Department of Mathematics, Payame Noor University (PNU), P. O. Box 19395-3697, Tehran, Iran

    Nader Kanzi

  2. Department of Economics, University of Messina, via dei Verdi, 75, Messina, Italy

    Giuseppe Caristi

  3. Department of Mathematics, Yazd Branch, Islamic Azad University, Yazd, Iran

    Ali Sadeghieh

Authors
  1. Nader Kanzi
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  2. Giuseppe Caristi
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  3. Ali Sadeghieh
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Correspondence to Nader Kanzi.

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Kanzi, N., Caristi, G. & Sadeghieh, A. Optimality conditions for semi-infinite programming problems involving generalized convexity. Optim Lett 13, 113–126 (2019). https://doi.org/10.1007/s11590-018-1256-8

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  • DOI: https://doi.org/10.1007/s11590-018-1256-8

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