Second-order necessary optimality conditions for semilinear elliptic optimal control problems |
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| Authors: | V. H. Nhu N. H. Son |
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| Affiliation: | 1. Department of Scientific Fundamentals, Posts and Telecommunications Institute of Technology, Hanoi, Vietnam.;2. School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, Hanoi, Vietnam. |
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| Abstract: | This paper deals with the necessary optimality conditions for semilinear elliptic optimal control problems with a pure pointwise state constraint and mixed pointwise constraints. By computing the so-called ‘sigma-term’, we obtain the second-order necessary optimality conditions for the problems, which is sharper than some previously established results in the literature. Besides, we give a condition which relaxes the Slater condition and guarantees that the Lagrangian is normalized. |
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| Keywords: | First-order necessary optimality condition second-order necessary optimality condition optimal control semilinear elliptic equation mixed pointwise constraint pure pointwise state constraint |
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