Global minima for semilinear optimal control problems

2015/03/24 by Ahmad Ahmad Ali, Ali, Ahmad Ahmad, Klaus Deckelnick +3 · 1 citation
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical methods for differential equations #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.1503.07086

openalex publication_date 2015/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider an optimal control problem subject to a semilinear elliptic PDE together with its variational discretization. We provide a condition which allows to decide whether a solution of the necessary first order conditions is a global minimum. This condition can be explicitly evaluated at the discrete level. Furthermore, we prove that if the above condition holds uniformly with respect to the discretization parameter the sequence of discrete solutions converges to a global solution of the corresponding limit problem. Numerical examples with unique global solutions are presented.

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