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Second-Order Optimality Conditions for Constrained Optimization Problems with \(C^1\) Data Via Regular and Limiting Subdifferentials

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Abstract

We present the second-order point-based (necessary and sufficient) optimality conditions for nonlinear programming with continuously differentiable data, via the regular and limiting (Mordukhovich) second-order subdifferentials. The sharper results are obtained for \(C^{1,1}\) data. Also, we derive a second-order characterization for (strictly and strongly) pseudoconvex, continuously differentiable functions.

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Acknowledgements

The authors would like to thank reviewers and the Guest Editor for valuable remarks and useful suggestions.

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Authors and Affiliations

  1. Department of Mathematics, University of Isfahan, 81745-163, Isfahan, Iran

    Mohammad Taghi Nadi

  2. Department of Mathematics, Sheikhbahaee University and University of Isfahan, Isfahan, Iran

    Jafar Zafarani

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  1. Mohammad Taghi Nadi
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  2. Jafar Zafarani
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Correspondence to Jafar Zafarani.

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Communicated by Boris S. Mordukhovich.

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Nadi, M.T., Zafarani, J. Second-Order Optimality Conditions for Constrained Optimization Problems with \(C^1\) Data Via Regular and Limiting Subdifferentials. J Optim Theory Appl 193, 158–179 (2022). https://doi.org/10.1007/s10957-021-01890-3

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