Abstract
In the present paper, we focus on the optimization problems, where objective functions are Fréchet differentiable, and whose gradient mapping is locally Lipschitz on an open set. We introduce the concept of second-order symmetric subdifferential and its calculus rules. By using the second-order symmetric subdifferential, the second-order tangent set and the asymptotic second-order tangent cone, we establish some second-order necessary and sufficient optimality conditions for optimization problems with geometric constraints. Examples are given to illustrate the obtained results.
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Acknowledgments
The authors would like to thank anonymous referees for their kind and helpful remarks and comments. This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) Under Grant Number 101.02-2012.03.
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Communicated by Nikolai Osmolovskii.
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Huy, N.Q., Tuyen, N.V. New Second-Order Optimality Conditions for a Class of Differentiable Optimization Problems. J Optim Theory Appl 171, 27–44 (2016). https://doi.org/10.1007/s10957-016-0980-4
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DOI: https://doi.org/10.1007/s10957-016-0980-4
Keywords
- Limiting normal cone
- Symmetric second-order subdifferential
- Second-order tangent set
- Local minimum point
- Second-order optimality conditions