REFERENCES
- F. Abergel and R. Temam ( 1990 ). On some optimal control problems in fluid mechanics . Theore. Computat. Fluid Mech. , 1(6): 303 – 325 .
- W. Alt ( 1990 ). The Lagrange-Newton Method for Infinite-Dimensional Optimization Problems . Numer. Funct. Anal. Optimiz. 11 : 201 – 224 . [CSA]
- P. Constantin and C. Foias ( 1988 ). Navier-Stokes Equations . Chicago : The University of Chicago Press .
- R. Dautray and J. L. Lions ( 2000 ). Mathematical Analysis and Numerical Methods for Science and Technology , Vol. 5. Berlin : Springer .
- M. Desai and K. Ito ( 1994 ). Optimal Controls of Navier-Stokes Equations . SIAM J. Control Optimiz. , 32: 1428 – 1446 . [CSA]
- A. Dontchev ( 1995 ). Implicit function theorems for generalized equations . Math. Program. 70 : 91 – 106 . [CSA]
- R. Griesse ( 2004 ). Parametric sensitivity analysis in optimal control of a reaction-diffusion system—Part I: Solution differentiability . Numer. Funct. Anal. Optimiz. , 25 ( 1–2 ): 93 – 117 . [CSA]
- R. Griesse ( 2005 ). Lipschitz Stability of Solutions to Some State-Constrained Elliptic Optimal Control Problems . Journal of Analysis and its Applications , to appear . [CSA]
- M. Gunzburger , L. Hou , and T. Svobodny ( 1991 ). Analysis and Finite Element Approximation of Optimal Control Problems for the Stationary Navier-Stokes Equations with Distribued and Neumann Controls . Math. Computat. 57 ( 195 ): 123 – 151 . [CSA]
- M. Gunzburger and S. Manservisi (2000). Analysis and approximation of the velocity tracking problem for Navier-Stokes Flows with distribued controls. SIAM J. Numer. Anal. 37(5):1481–1512. [CSA] [CROSSREF]
- M. Gunzburger and S. Manservisi ( 2000 ). The Velocity tracking problem for navier-Stokes flows with boundary control . SIAM J. Control Optimiz. 39 ( 2 ): 594 – 634 . [CSA] [CROSSREF]
- M. Hintermüller and M. Hinze An SQP Semi-Smooth Newton-Type Algorithm Applied to the Instationary Navier-Stokes System Subject to Control Constraints . SIAM J. Optimiz. , to appear . [CSA]
- M. Hinze ( 2000 ). Optimal and Instantaneous Control of the Instationary Navier–Stokes Equations . Habilitation Thesis; Berlin : Fachbereich Mathematik, Technische Universität .
- M. Hinze and K. Kunisch ( 2001 ). Second order methods for optimal control of time-dependent fluid flow . SIAM J. Control Optimiz. 40 ( 3 ): 925 – 946 . [CSA] [CROSSREF]
- J. L. Lions ( 1969 ). Quelques méthodes de résolution des problemès aux limites non linéaires . Paris : Dunod Gauthier-Villars .
- K. Malanowski ( 2002 ). Sensitivity analysis for parametric optimal control of semilinear parabolic equations . J. Convex Anal. 9 ( 2 ): 543 – 561 . [CSA]
- K. Malanowski ( 2003 ). Solution differentiability of parametric optimal control for elliptic equations . In: Sachs E. W. Tichatschke R. eds., System Modeling and Optimization XX . Proceedings of the 20th IFIP TC 7 Conference . Kluwer Academic Publishers , pp. 271 – 285 .
- K. Malanowski and F. Tröltzsch ( 1999 ). Lipschitz stability of solutions to parametric optimal control for parabolic equations . J. Analy. Appli. 18 ( 2 ): 469 – 489 . [CSA]
- K. Malanowski and F. Tröltzsch ( 2000 ). Lipschitz stability of solutions to parametric optimal control for elliptic equations . Control Cybernetics , 29: 237 – 256 . [CSA]
- P. Neittaanmäki and D. Tiba ( 1994 ). Optimal Control of Nonlinear Parabolic Systems . New York : Marcel Dekker .
- S. Robinson ( 1980 ). Strongly regular generalized equations . Math. Oper. Res. 5 ( 1 ): 43 – 62 . [CSA]
- T. Roubíček and F. Tröltzsch ( 2003 ). Lipschitz stability of optimal controls for the steady-state Navier-Stokes equations . Control Cybernetics , 32(3): 683 – 705 . [CSA]
- R. Temam ( 1984 ). Navier-Stokes Equations, Theory and Numerical Analysis . Amsterdam : North-Holland .
- F. Tröltzsch ( 2000 ). Lipschitz stability of solutions of linear-quadratic parabolic control problems with respect to perturbations . Dynamics of Continuous, Discrete and Impulsive Systems, Series A, Mathematical Analysis 7 ( 2 ): 289 – 306 . [CSA]
- F. Tröltzsch and S. Volkwein ( 2001 ). The SQP Method for Control Constrained Optimal Control of the Burgers Equation . European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimisation and Calculus of Variations 6 : 649 – 674 . [CSA]
- F. Tröltzsch and D. Wachsmuth ( 2005 ). Second-order sufficient optimality conditions for the optimal control of Navier-Stokes equations . ESAIM: Control, Optimisation and Calculus of Variations , to appear . [CSA]
- M. Ulbrich ( 2003 ). Constrained optimal control of Navier-Stokes flow by semismooth Newton methods . Systems Control Lett. 48 : 297 – 311 . [CSA] [CROSSREF]
- D. Wachsmuth ( 2005 ). Regularity and stability of optimal controls of instationary Navier-Stokes equations . Control Cybernetics 34 : 387 – 410 . [CSA]