Error estimates for the discretization of state constrained convex control problems

Numerical Functional Analysis and Optimization

Volumn 17, Issue 9-10, 1996, Pages 1005-1028

  Tiba, D ^a   Troltzsch F ^b  

^a INSTITUTE OF MATHEMATICS   (Romania)

^b CHEMNITZ UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000197665     PISSN: 01630563     EISSN: None     Source Type: Journal    
DOI: 10.1080/01630569608816739     Document Type: Article

References (15)

1. Alt, W.: On the approximation of infinite optimization problems with an application to optimal control problems. Applied Math. Optimization 22(1991), 83-98.
2. Alt, W., Markenroth, U.: Convergence of finite element approximations to state constrained convex parabolic boundary control problems, SIAM J. Control and Optimiz., vol. 27(4), p. 718-736 (1989).
3. Amann, H.: Parabolic evolution equation with nonlinear boundary conditions. In: F.E. Browder, Editor, Nonlinear Functional Analysis Proc. Sympos. Pure Math. Vol. 45, Part. I, AMS Publications, Providence 1986.
4. Barbu, V., Precupanu, Th.: Convexity and optimization in Banach spaces, Sijthoff & Nordhoff, Leyden (1978).
5. Knowles, G.: Finite element approximation of parabolic time optimal control problems. SIAM J. Control Opt. 20(1982), 414-427.
6. French, D.A., King, J.T.: Approximation of an elliptic control problem by the finite element method, Numer. Funct. Anal. Appl. 12 (1991), 299-315.
7. Lions, J. L.: Contrôle optimal des systèmes gouvernés par des équations aux dérivés partielles, Dunod, Paris 1968.
8. Lasiecka, I.: State constrained control problems for parabolic systems: regularity of optimal solutions, Applied Math. Optimization (1980).
9. Lasiecka, I.: Ritz-Galerkin approximation of the time optimal boundary control problem for parabolic systems with Dirichlet boundary conditions, SIAM J. Control Optim. 22(1984), 477-500.
10. Malanowski, K.: Convergence of approximations vs. regularity of solutions for convex, control-constrained optimal control problems, Appl. Math. Optim. 8(1981), 69-95.
11. Pawlow, I.: Analysis and control of evolution multi-phase problems with free boundaries, Ossolineum, Warszawa (1987).
12. Tiba, D., Neittaanmäki, P.: Optimal control of nonlinear parabolic equations. Theory, algorithms and applications, Marcel Dekker, New York (1994).
13. Tröltzsch, F.: Optimality conditions for parabolic control problems and applications", Teubner Texte, Leipzig 1984.
14. Tröltzsch, F.: Approximation of nonlinear parabolic boundary control problems by the Fourier method - convergence of optimal controls, Optimization 22(1991), 83-98.
15. Tröltzsch, F.: Semidiscrete Ritz-Galerkin approximation of nonlinear parabolic boundary control problems - strong convergence of optimal controls, Applied Math. Optimization 29(1994), 309-329.