On an augmented Lagrangian SQP method for a class of optimal control problems in Banach spaces

Computational Optimization and Applications

Volumn 22, Issue 3, 2002, Pages 369-398

  Arada, Nadir ^a   Raymond, Jean Pierre ^b   TröLtzsch, Fredi ^c  

^a CHEMNITZ UNIVERSITY OF TECHNOLOGY   (Germany)

^b CNRS   (France)

^c TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Augmented Lagrangian SQP method in Banach spaces; Control constraints; Generalized equation; Generalized Newton method; Optimal control; Semilinear parabolic equation; Two norm discrepancy

Indexed keywords

BOUNDARY CONDITIONS; CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; NONLINEAR SYSTEMS; OPTIMAL CONTROL SYSTEMS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING; SET THEORY;

GENERALIZED NEWTON METHODS;

QUADRATIC PROGRAMMING;

EID: 0036737318     PISSN: 09266003     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1019763022415     Document Type: Article

References (30)

1. J.J. Alibert and J.P. Raymond, "A Lagrange multiplier theorem for control problems with state constraints," Numer. Funct. Anal. and Optimiz., vol. 19, pp. 697-704, 1998.
2. W. Alt, "The Lagrange-Newton method for infinite-dimensional optimization problems," Numer. Funct. Anal. and Optimiz., vol. 11, pp. 201-224, 1990.
3. W. Alt, "The Lagrange Newton method for infinite-dimensional optimization problems," Control and Cybernetics, vol. 23, pp. 87-106, 1994.
4. W. Alt, "Discretization and mesh independence of Newton's method for generalized equations," in Mathematical Programming with Data Perturbation. A.K. Fiacco (Ed.), Lecture Notes in Pure and Appl. Math., Marcel Dekker: New York, vol. 195, 1998, pp. 1-30.
5. V. Barbu, Analysis and Control of Nonlinear Infinite Dimensional Systems, Academic Press: Boston, 1993.
6. M. Bergounioux and K. Kunisch, "Augmented Lagrangian techniques for elliptic state constrained optimal control problems," SIAM J. Control Optim., vol. 35, pp. 1524-1543, 1997.
7. D.B. Bertsekas, "Projected Newton methods for optimization problems with simple constraints," SIAM J. Control Optim., vol. 20, pp. 221-246, 1982.
8. E. Casas, "Pontryagin's principle for state-constrained boundary control problems of semilinear parabolic equations," SIAM J. Control Optim., vol. 35, pp. 1297-1327, 1997.
9. H. Goldberg and F. Tröltzsch, "Second order sufficient optimality conditions for a class of nonlinear parabolic boundary control problems" SIAM J. Control Optimization, vol. 31, pp. 1007-1025, 1993.
10. H. Goldberg and F. Tröltzsch, "On a SQP-Multigrid technique for nonlinear parabolic boundary control problems," in Optimal Control: Theory, Algorithms, and Applications, W.W. Hager and P.M. Pardalos (Eds.), Kluwer Academic Publishers B.V., 1998, pp. 154-177.
11. W.W. Hager, "Approximations to the multiplier method," SIAM J. Numer. Analysis, vol. 22, pp. 16-46, 1985.
12. W.W. Hager, "Multiplier methods for nonlinear optimal control" SIAM J. Control Optimization, vol. 27, pp. 1061-1080, 1990.
13. M. Heinkenschloss and E.W. Sachs, "Numerical solution of a constrained control problem for a phase field model," Control and Estimation of Distributed Parameter Systems, Int. Ser. Num. Math., vol. 118, pp. 171-188, 1994.
14. A.D. Ioffe, "Necessary and sufficient conditions for a local minimum, part 3: Second order conditions and augmented duality," SIAM J. Control Optimization, vol. 17, pp. 266-288, 1979.
15. A.D. Ioffe and Tikhomirov, Theory of Extremal Problems, North Holland: Amsterdam, 1979.
16. K. Ito and K. Kunisch, "Augmented Lagrangian-SQP methods for nonlinear optimal control problems of tracking type," SIAM J. Control Optim., vol. 34, pp. 874-891, 1996.
17. K. Ito and K. Kunisch, "Augmented Lagrangian-SQP methods in Hilbert spaces and application to control in the coefficients problems," SIAM J. Optim., vol. 6, pp. 96-125, 1996.
18. A. Kauffmann, "Optimal control of the solid fuel ignition model," Thesis, Technical University of Berlin, Oct. 1998.
19. K. Kunisch and S. Volkwein, "Augmented Lagrangian-SQP techniques and their approximations," Contemporary Mathematics, vol. 209, pp. 147-159, 1997.
20. O.A. Ladyzenskaja, V.A. Solonnikov, and N.N. Ural'ceva, "Linear and quasilinear equations of parabolic type," Translations of Mathematical Monographs, 23, Amer. Math. Soc., Providence, R.I., 1968.
21. H. Maurer, "First and second order sufficient optimality conditions for infinite-dimensional programming problems," Math. Programming, vol. 16, pp. 98-110, 1979.
22. H. Maurer and J. Zowe, "First and second-order necessary and sufficient optimality conditions in mathematical programming and optimal control," Math. Programming Study, vol. 14, pp. 163-177, 1981.
23. J.P. Raymond and F. Tröltzsch, "Second order sufficient optimality conditions for nonlinear parabolic control problems with state constraints," Disc. Cont. Dyn. Systems, vol. 6, pp. 431-450, 2000.
24. J.P. Raymond and H. Zidani, "Hamiltonian Pontryagin's principles for control problems governed by semilinear parabolic equations," Appl. Math. Optim., vol. 39, pp. 143-177, 1999.
25. S.M. Robinson, "Strongly regular generalized equations," Math. of Operations Research, vol. 5, pp. 43-62, 1980.
26. F. Tröltzsch, "On the Lagrange-Newton method for the optimal control of semilinear parabolic equations," SIAM J. Optim., vol. 38, pp. 294-312, 1999.
27. F. Tröltzsch, "Lipschitz stability of solutions to linear-quadratic parabolic control problems with respect to perturbations," Dynamics of Continuous, Discrete and Impulsive Systems, vol. 7, pp. 289-306, 2000.
28. A. Unger, "Hinreichende Optimalitätsbedingungen 2. Ordnung und Konvergenz des SQP-Verfahrens für semilineare elliptische Randsteuerprobleme," Thesis, Technical University of Chemnitz, Dec. 1997
29. S. Volkwein, "Mesh-independence for an augmented Lagrangian-SQP method in Hilbert spaces," SIAM J. Optim., vol. 38, pp. 767-785, 2000.
30. S. Volkwein, "Distributed control problems for the Burgers equation," Computational Optimization and Applications, vol. 18, pp. 115-140, 2001.