Second-order optimality conditions for semilinear elliptic control problems with constraints on the gradient of the state

Control and Cybernetics

Volumn 28, Issue 3, 1999, Pages 462-479

  Casas, E ^a   Fernandez L A ^a   Mateos, M ^b  

^a UNIVERSITY OF CANTABRIA   (Spain)

^b UNIVERSITY OF OVIEDO   (Spain)

Author keywords

Optimal control; Second order conditions; Semilinear elliptic PDE; State gradient constraints

Indexed keywords

EID: 0345854815     PISSN: 03248569     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (8)

1. BONNANS, J.F. and CASAS, E. (1988) Contrôle de systèmes elliptiques semilinéaires comportant des contraintes sur l'état. In: H. Brezis and J.L. Lions, eds., Nonlinear Partial Differential Equations and Their Applications. Collège de France Seminar, 8, pp. 69-86. Longman Scientific & Technical, New York.
2. CARTAN, H. (1967) Calcul Différentiel Hermann, Paris.
3. CASAS, E. and TRÖLTZSCH, F. (1999) Second order necessary and sufficient optimality conditions for optimization problems and applications to control theory. To appear.
4. CLARKE, F.H. (1976) A new approach to lagrange multipliers. Mathematics in Operations Research, 1, 2, 165-174.
5. IOFFE, A. (1979) Necessary and sufficient conditions for a local minimum 3: second order conditions and augmented duality. SIAM J. Control Optim., 17, 266-288.
6. MATEOS, M. (2000) Problemas de Control Optimo Gobernados por Ecuaciones Semilineales con Restricciones de Tipo Integral sobre el Gradiente del Estado. PhD thesis, Universidad de Cantabria. To appear.
7. MAURER, H. (1981) First and second order sufficient optimality conditions in mathematical programming and optimal control. Math. Programming Study, 14, 163-177.
8. STAMPACCHIA, G. (1965) Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus. Ann. Inst. Fourier (Grenoble), 15, 189-258.