Global minima for semilinear optimal control problems

Ahmad Ahmad Ali, Klaus Deckelnick and Michael Hinze ()
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Ahmad Ahmad Ali: Universität Hamburg
Klaus Deckelnick: Otto-von-Guericke-Universität Magdeburg
Michael Hinze: Universität Hamburg

Computational Optimization and Applications, 2016, vol. 65, issue 1, No 9, 288 pages

Abstract: 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.

Keywords: Optimal control; Semilinear PDE; Uniqueness of global solutions; Second order sufficient condition; Gagliardo–Nirenberg inequality; 49J20; 35K20; 49M05; 49M25; 49M29; 65M12; 65M60 (search for similar items in EconPapers)
Date: 2016
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10589-016-9833-1

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