2019/02/25 by Ahmad Ahmad Ali, Ali, A. Ahmad, Klaus Deckelnick +3
Engineering · Mathematics · #35K20 #49J20 #49M05 #49M25 #49M29 #65M12 #65M60 #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Numerical methods for differential equations #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1902.09639
openalex publication_date 2019/02/25 · openalex created_date 2019/03/02 · openalex updated_date 2026/07/28
We consider a C1-semilinear elliptic optimal control problem possibly subject to control and/or state constraints. Generalizing previous work we provide a condition which guarantees that a solution of the necessary first order conditions is a global minimum. A similiar result also holds at the discrete level where the corresponding condition can be evaluated explicitly. Our investigations are motivated by Günter Leugering, who raised the question whether our previous results can be extended to the nonlinearity ϕ(s)=s|s|. We develop a corresponding analysis and present several numerical test examples demonstrating its usefulness in practice.