Abstract
In this paper, new second-order set-valued directional derivatives are proposed for C\(^1\) functions, whose derivative is locally calm (stable), in normed spaces. Its existence, main calculus, as well as Taylor’s expansions are studied. We then employ them to investigate optimality conditions for optimization problems with geometric and functional constraints. The results also improve the corresponding ones for problems involving C\(^{1,1}\) functions. Examples that analyze and illustrate our results are given.
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The authors are very grateful to the Editors and the Anonymous Referees for their valuable suggestions and remarks leading to the significant improvement of the paper.
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Tung, N.M., Bao, N.X.D. New second-order limiting directional derivatives and C\(^1\)-optimization. Optim Lett 17, 1791–1810 (2023). https://doi.org/10.1007/s11590-022-01956-9
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DOI: https://doi.org/10.1007/s11590-022-01956-9