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Necessary and Sufficient Conditions for (Weakly) Efficient of Non-Differentiable Multi-Objective Semi-Infinite Programming Problems

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Abstract

We consider a multi-objective semi-infinite programming problem with a feasible set defined by inequality constraints. First, we present a Fritz–John type necessary optimality condition. Then, we introduce two constraint qualifications and derive the weak and strong Karush–Kuhn–Tucker types necessary conditions for (weakly) efficient solution of the considered problem. Finally, an extension of a Caristi–Ferrara–Stefanescu result for the (\(\Phi\), \(\rho\))-invexity is proved, and some sufficient conditions are presented under this weak assumption. All results are given in term of Clarke subdifferential.

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Acknowledgements

The author would like to expresses his gratitude to the anonymous referees for helpful comments on the first version of the paper.

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  1. Department of Mathematics, Payame noor University (PNU), Tehran, Iran

    Nader Kanzi

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  1. Nader Kanzi
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Correspondence to Nader Kanzi.

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Kanzi, N. Necessary and Sufficient Conditions for (Weakly) Efficient of Non-Differentiable Multi-Objective Semi-Infinite Programming Problems. Iran J Sci Technol Trans Sci 42, 1537–1544 (2018). https://doi.org/10.1007/s40995-017-0156-6

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  • DOI: https://doi.org/10.1007/s40995-017-0156-6

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