Parametric sensitivity analysis in optimal control of a reaction-diffusion system - Part II: Practical methods and examples

Optimization Methods and Software

Volumn 19, Issue 2, 2004, Pages 217-242

  Griesse, Roland ^a  

^a UNIVERSITY OF GRAZ   (Austria)

Author keywords

Control constraints; Optimal control; Parameter perturbation; Parametric sensitivity; Reaction diffusion equations

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; CONSTRAINT THEORY; DIFFUSION; MATHEMATICAL MODELS; MATRIX ALGEBRA; OPTIMIZATION; PERTURBATION TECHNIQUES; SENSITIVITY ANALYSIS;

CONTROL CONSTRAINTS; OPTIMAL CONTROL; PARAMETER PERTURBATION; PARAMETRIC SENSITIVITY; REACTION-DIFFUSION EQUATIONS;

OPTIMAL CONTROL SYSTEMS;

EID: 1842764942     PISSN: 10556788     EISSN: None     Source Type: Journal    
DOI: 10.1080/10556780410001654250     Document Type: Article

References (17)

1. R. Griesse (2003). Parametric sensitivity analysis in optimal control of a reaction-diffusion system - Part I: Solution differentiability. Report No. 269, Special Research Center F003, Project Area II: Continuous Optimization and Control, University of Graz & Technical University of Graz, Austria, http://www.staff.unibayreuth.de/~btmn07 (submitted).
2. R. Griesse (2003). Parametric sensitivity analysis for control-constrained optimal control problems governed by systems of parabolic partial differential equations. PhD Thesis, Universität Bayreuth.
3. W. Hager (2000). Runge-Kutta methods in optimal control and the transformed adjoint system. Numerische Mathematik, 87, 247-282.
4. D. Braess (1997). Finite Elemente. Springer, Berlin.
5. G. Golub and C. van Loan (1983). Matrix Computations. Johns Hopkins University Press, Baltimore.
6. J. Nocedal and S. Wright (1999). Numerical Optimization. Springer, New York.
7. R. Griesse and A. Walther (2002). Parametric sensitivity analysis for optimal control problems using automatic differentiation. Optimal Control Applications and Methods (to appear).
8. 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.
9. M. Bergounioux, M. Haddou, M. Hintermüller and K. Kunisch (2000). A comparison of a Moreau-Yosida-based active set strategy and interior point methods for constrained optimal control problems. SIAM Journal on Optimization, 11, 495-521.
10. M. Bergounioux, K. Ito and K. Kunisch (1999). Primal-dual strategy for constrained optimal control problems. SIAM Journal on Control and Optimization, 37, 1176-1194.
11. K. Ito and K. Kunisch (2002). The primal-dual active set method for nonlinear optimal control problems with bilateral constraints. SIAM Journal on Control and Optimization (to appear).
12. K. Jittorntrum (1984). Solution point differentiability without strict complementarity in nonlinear programming. Mathematical Programming Study, 21, 127-138.
13. D. O'Leary (1980). The block conjugate gradient algorithm and related methods. Linear Algebra and its Applications, 29, 293-322.
14. C. Büskens and R. Griesse (2002). Computational parametric sensitivity analysis of perturbed PDE optimal control problems with state and control constraints, http://www.staff.uni-bayreuth.de/~btmn07 (submitted).
15. C. Büskens and H. Maurer (2001). Sensitivity analysis and real-time control of parametric optimal control problems using nonlinear programming methods. Online Optimization of Large Scale Systems. pp. 57-68, Springer.
16. H. J. Pesch (1989). Real-time computation of feedback controls for constrained optimal control problems, Part 1: Neighboring extremals. Optimal Control Applications & Methods, 10, 129-145.
17. H. J. Pesch (1989). Real-time computation of feedback controls for constrained optimal control problems, Part 2: A correction method based on multiple shooting. Optimal Control Applications & Methods, 10, 147-171.