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Positivity

, Volume 23, Issue 1, pp 195–217 | Cite as

Sequence-based necessary second-order optimality conditions for semilinear elliptic optimal control problems with nonsmooth data

  • Tuan Nguyen DinhEmail author
Article
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Abstract

The main goal of this note is to formulate sequence-based necessary second-order optimality conditions for a semilinear elliptic optimal control problem, with a pointwise pure state constraint and a pointwise mixed state-control constraint, governed by nonsmooth functions. Using a modification of the Dubovitskii–Milyutin scheme, we develop necessary second-order conditions for optimality, which depend on given sequences, in terms of sequential tangent sets and sequential directional derivatives for not necessarily twice differentiable mappings.

Keywords

Nonsmooth optimal control Sequence-based necessary optimality condition Semilinear elliptic equation Pointwise pure state constraint Pointwise mixed state-control constraint 

Mathematics Subject Classification

35J25 49K20 49K27 90C29 90C46 

Notes

Acknowledgements

The author would like to thank the editor and an anonymous referee for their valuable remarks and suggestions, which have helped him to improve the presentation of the paper.

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Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of Economics-Hochiminh CityHochiminh CityVietnam

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