Geodesic
Necessary and Sufficient Optimality Conditions for Optimization Problems in Function Spaces and Applications to Control Theory
E. Casas1 ; Mariano Mateos2 ; Fredi Tröltzsch3
1 Departamento de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. Industriales y de Telecomunicación, Universidad de Cantabria, 39005 Santander, Spain ,
2 Departamento de Matemáticas, EUIT Industriales, Universidad de Oviedo., Spain,
3 Fakultät für Mathematik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany,
ESAIM. Proceedings, Tome 13 (2003), pp. 18-30.

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We consider an abstract formulation for optimization problems in some Lp spaces. The variables are restricted by pointwise upper and lower bounds and by finitely many equality and inequality constraints of functional type. Second-order necessary and sufficient optimality conditions are established, where the cone of critical directions is arbitrarily close to the form which is expected from the optimization in finite dimensional spaces. The results are applied to an optimal control problem governed by a partial differential equation. Finally we compare the conditions obtained by applying this abstract procedure and those ones derived by using the methods adapted to the optimal control problem.
DOI : 10.1051/proc:2003001

E. Casas 1 ; Mariano Mateos 2 ; Fredi Tröltzsch 3

1 Departamento de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. Industriales y de Telecomunicación, Universidad de Cantabria, 39005 Santander, Spain ,
2 Departamento de Matemáticas, EUIT Industriales, Universidad de Oviedo., Spain,
3 Fakultät für Mathematik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany, 
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     author = {E. Casas and Mariano Mateos and Fredi Tr\"oltzsch},
     title = {Necessary and {Sufficient} {Optimality} {Conditions} for {Optimization} {Problems} in {Function} {Spaces} and {Applications} to {Control} {Theory}},
     journal = {ESAIM. Proceedings},
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E. Casas; Mariano Mateos; Fredi Tröltzsch. Necessary and Sufficient Optimality Conditions for Optimization Problems in Function Spaces and Applications to Control Theory. ESAIM. Proceedings, Tome 13 (2003), pp. 18-30. doi : 10.1051/proc:2003001. http://geodesic.mathdoc.fr/articles/10.1051/proc:2003001/

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