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Bibliography

1
N. Arada, J.-P. Raymond, and F. Troltzsch, On an augmented Lagrangian SQP method for a class of optimal control problems in Banach spaces, to appear.

2
J.F. Bonnans, Second-order analysis for control constrained optimal control problems of semilinear elliptic systems, Appl. Math. Optim., 38, (1998), 303-325.

3
Ch. Buskens and H. Maurer, SQP-methods for solving optimal control problems with control and state constraints; adjoint variables, sensitivity analysis, and real-time control, J. Comp. Appl. Math. 120, (2000), 85-108.

4
E. Casas, F. Troltzsch, and A. Unger, Second order sufficient optimality conditions for a nonlinear elliptic control problem, J. Anal. Appl., 15, (1996), 687-707.

5
E. Casas, F. Troltzsch, and A. Unger, Second order sufficient optimality conditions for some state-constrained control problems of semilinear elliptic equations, to appear in SIAM J. Control Optim.

6
A.L. Dontchev, W.W. Hager, A.B. Poore, and B. Yang, Optimality, stability, and convergence in optimal control, Appl. Math. Optim., 31, (1995), 297-326.

7
R. Fourer, D.M. Gay, and B.W. Kernighan, AMPL: A modeling language for mathematical programming, Duxbury Press, Brooks/Cole Publishing Company, Pacific Grove, CA, 1993.

8
H. Goldberg and F. Troltzsch, Second order sufficient optimality conditions for a class of nonlinear parabolic boundary control problems, SIAM J. Control Optim., 31, (1993), 1007-1025.

9
H. Goldberg and F. Troltzsch, On a Lagrange-Newton method for a nonlinear parabolic boundary control problem, Optim. Meth. Software, 8, (1998), 225-247.

10
M. Heinkenschloss, SQP interior-point methods for distributed optimal control problems, to appear in Encyclopedia of Optimization, P. Pardalos and C. Floudas (eds.), Kluwer Academic Publishers.

11
A.D. Ioffe, Necessary and sufficient conditions for a local minimum, part 3: Second order conditions and augmented duality, SIAM J. Control Optim., 17, (1979), 266-288.

12
K. Ito and K. Kunisch, Augmented Lagrangian-SQP methods for nonlinear optimal control problems of tracking type, SIAM J. Control Optim., 34, (1996), 874-891.

13
K. Ito and K. Kunisch, The Newton algorithm for a class of weakly singular optimal control problems, to appear in SIAM J. Optim.

14
K. Malanowski, Sufficient optimality conditions for optimal control problems subject to state constraints, SIAM J. Control Optim., 35, (1997), 205-227. 1994.

15
H. Maurer, First and second order sufficient optimality conditions in mathematical programming and optimal control, Math. Programming Study, 14, (1981), 163-177.

16
H. Maurer and H.D. Mittelmann, Optimization techniques for solving elliptic control problems with control and state constraints. Part I: Boundary control, Comp. Optim. Appl., 16, (2000), 29-55.

17
H. Maurer and H.D. Mittelmann, Optimization techniques for solving elliptic control problems with control and state constraints. Part II: Distributed control, to appear in Comp. Optim. Appl.

18
H.D. Mittelmann and H. Maurer, Solving elliptic control problems with interior and SQP methods: control and state constraints, J. Comp. Appl. Math. 120, (2000), 175-195.

19
H.D. Mittelmann, Verification of Second-Order Sufficient Optimality Conditions for Semilinear Elliptic and Parabolic Control Problems, to appear in Comp. Optim. Appl.

20
H. Maurer and S. Pickenhain, Second-order sufficient conditions for control problems with mixed control-state constraints, J. Optim. Theory Appl., 86, (1995), 649-667.

21
J.-P. Raymond and F. Troltzsch, Second order sufficient optimality conditions for nonlinear parabolic control problems with state constraints, to appear.

22
Th.H. Robey and D.L. Sulsky, Row ordering for Sparse QR Decomposition, SIAM J. Matrix Anal. Applic., 15, (1994), 1208-1225.

23
K. Schittkowski, Numerical solution of a time-optimal parabolic boundary-value control problem, J. Optim. Theory Appl., 27, (1979), 271-290.

24
V.H. Schulz (ed.), SQP-based direct discretization methods for practical optimal control problems, J. Comp. Appl. Math. 120, (2000) (special issue).

25
A.R. Shenoy, M. Heinkenschloss, and E.M. Cliff, Airfoil design by an all-at-once method, Intern. J. Comp. Fluid Dynam., 11, (1998), 3-25.

26
P. Spellucci, Numerische Verfahren der nichtlinearen Optimierung, Birkhäuser-Verlag, Basel, 1993.

27
R.J. Vanderbei and D.F. Shanno, An interior-point algorithm for nonconvex nonlinear programming, Comp. Optim. Appl., 13, (2000), 231-252.

28
S. Volkwein, Distributed control problems for the Burgers equation, to appear in Comp. Optim. Applic.

29
S. Volkwein, Application of augmented Lagrangian-SQP methods to optimal control problems for the stationary Burgers equation, to appear in Comp. Optim. Applic.

30
S. Volkwein, Mesh-Independence for an Augmented Lagrangian-SQP Method in Hilbert Spaces, to appear in SIAM J. Control Optim.

31
V. Zeidan, The Riccati equation for optimal control problems with mixed state-control constraints: Necessity and Sufficiency, SIAM J. Control Optim., 32, (1994), 1297-1321.



Hans Mittelmann
2000-08-31