Optimality conditions and generalized bang-bang principle for a state-constrained semilinear parabolic problem

Numerical Functional Analysis and Optimization

Volumn 17, Issue 5-6, 1996, Pages 517-536

  Bergounioux, M ^a   Troltzsch F ^b  

^a UNIVERSITÉ D'ORLÉANS   (France)

^b CHEMNITZ UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001204135     PISSN: 01630563     EISSN: None     Source Type: Journal    
DOI: 10.1080/01630569608816708     Document Type: Article

References (16)

1. D. Azé, On Optimality Conditions for State-Constrained Optimal Control Problems Governed by Partial Differential Equations, Preprint (1995).
2. V. Barbu, Nonlinear semigroups and differential equations in Banach spaces, Noordhoff, Leyden, the Netherlands (1976).
3. V. Barbu and Th. Precupanu, Convexity and optimization in Banach spaces, Sijthoff and Noordhoff, Leyden, the Netherlands (1978).
4. M. Bergounioux, A penalization method for optimal control of elliptic stationnary problems with state constraints , SIAM Journal on Control and Optimization, Vol 30 , no 2 , pp. 305-323 (1992).
5. M. Bergounioux, Distributed and initial control of semilinear parabolic systems, Optimization, Vol 33, no 4, pp. 339-358 (1995).
6. M. Bergounioux and D. Tiba, General optimality conditions for constrained convex control problems, SIAM Journal on Control and Optimization, (1996).
7. H. Brezis, Analyse fonctionnelle. Théorie et applications, Masson, Paris (1983).
8. E. Di Benedetto, On the local behaviour of solutions of degenerate parabolic equations with measurable coefficients, Annali della Scuola Normale Superiore di Pisa, Ser. I, Vol 13, no 3, pp. 487-535 (1986).
9. A.D. Ioffe and V.M. Tikhomirov, Theory of extremal problems, North-Holland, Amsterdam (1979) (Translation from the Russian).
10. P. Neittaanmäki and D. Tiba, Optimal control of nonlinear parabolic systems, Marcel Dekker, New-York (1994) .
11. J.L. Lions, Quelques méthodes de résolution de Problèmes aux limites non linéaires, Dunod, Paris (1969).
12. J.L. Lions, Control of distributed singular systems, Dunod,Gauthier-Villars Paris (1985).
13. D. Tiba, Optimal control of nonsmooth distributed parameter systems, Lecture Notes in Mathematics no 1459, Springer-Verlag, Berlin (1990).
14. F. Tröltzsch, Optimality conditions for parabolic control problems and applications, Teubner Texte zur Mathematik, Leipzig (1984).
15. F. Tröltzsch, A modification of the Zowe and Kurcyusz regularity condition with application to the optimal control of Noether operator equations with constraints on the control and the state, Math. Operationforsch. Statist., Ser. Optimization, Vol 14, no 2, pp. 245-253 (1983).
16. J. Zowe and S. Kurcyusz, Regularity and stability for the mathematical programming problem in Banach spaces, Applied Mathematics and Optimization, 5, pp.49-62 (1979).