Preview
Unable to display preview. Download preview PDF.
References
F.H. Clarke: Optimization and Nonsmooth Analysis, J. Wiley and Sons, New York, 1983.
A.L. Dontchey: Perturbations, Approximations and Sensitivity Analysis of Optimal Control Systems. Lecture Notes in Control and Information Sciences, Vol. 52, Springer, Berlin, Heidelberg, New York, Tokyo, 1983.
N. Dunford, J.T. Schwartz: Linear Operators. Part I, Interscience Publishers Inc., New York, 1958.
B. Gollan: On the Optimal Value Function of Optimal Control Problems, Zeitschrift fur Analysis und ihre Ahwendingen, 1 (1982), 17–33.
W.W. Hager: Lipschitz Continuity for Constrained Processes. SIAM J. Control 17 (1979) 321–337.
A. Haraux: Dérivation Dans les Inéquations Variationelles, CR Acad. Sci., Serie A, 278 (1974) 1257–1260.
K. Jittorntrum: Solution Point Differentiability without Strict Complementarity in Nonlinear Programming, in: Mathematical Programming Study 21, A.V. Fiacco (Ed.), Amsterdam 1984, pp. 127–138.
O.A. Ladyženskaja, V.A. Solonnikov, N.N. Uraltzeva: Linear and Quasilinear Equations of Parabolic Type, Nauka, Moscow, 1967 (in Russian).
I. Lasiecka, K. Malanowski: On Regularity of Solutions to Convex Optimal Control Problems with Control Constraints for Parabolic Systems, Contr. and Cybern. 6 (1977), No.3–4, 57–74.
F. Lempio, H. Maurer: Differential Stability in Infinite-Dimensional Nonlinear Programming, Appl. Math. Optim. 6 (1980) 139–152.
J.L. Lions: Contrôl Optimal de Systèmes Gouvernés par des Équations aux Dérivées Partielles, Dunod, Paris, 1968.
J.L. Lions, E. Magenes: Problemes aux Limites Non Homogenes et Applicationes, Vol. 1, Dunod, Paris, 1968.
K. Malanowski: Differential Stability of Solutions to Convex, Control Constrained Optimal Control Problems, Appl. Math. Optim. 12 (1984) 1–14.
K. Malanowski, J. Sokołowski: Sensitivity of Solutions to Convex, Control Constrained Optimal Control Problems for Distributed Parameter Systems (to be published).
H. Maurer: Differential Stability in Optimal Control Problems, Appl. Math. Optim. 5 (1979), 283–295.
F. Mignot: Contrôle dans les Inéqualitions Variationelles, J. Functional Anal. 22 (1976), 130–185.
J. Sokołowski: Sensitivity Analysis of Control Constrained Optimal Control Problems for Distributed Systems (to be published).
J. Sokołowski: Differential Stability of Solutions to Constrained Optimization Problems, Rapport de Recherche No. 312, Institut National de Recherche en Informatique et en Automatique, Rocquencourt, 1984.
J. Sokołowski: Differential Stability of Control Constrained Optimal Control Problems for Distributed Parameter Systems, in: Proceedings of 2nd International Conference on Control Theory for Distributed Parameter Systems and Applications, Vorau, Austria, July 9–14, 1984 (to be published).
Editor information
Rights and permissions
Copyright information
© 1986 Springer-Verlag
About this paper
Cite this paper
Malanowski, K. (1986). Sensitivity of solutions to convex optimal control problems for parabolic equations. In: Malanowski, K., Mizukami, K. (eds) Analysis and Algorithms of Optimization Problems. Lecture Notes in Control and Information Sciences, vol 82. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0007155
Download citation
DOI: https://doi.org/10.1007/BFb0007155
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16660-3
Online ISBN: 978-3-540-39844-8
eBook Packages: Springer Book Archive