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M. Bergounioux, M. Haddou, M. Hintermüller and K. Kunisch,
``A comparison of interior point methods and a Moreau-Yosida based
active set strategy for constrained optimal control problems'',
Preprint, Université d`Orléans, Orléans, France, 1998.
- 2
-
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.
- 3
-
M. Bergounioux, K. Ito and K. Kunisch,
``Primal-dual strategy for constrained optimal control problems'',
Karl-Franzens-Universität Graz & Technische Universität Graz,
Spezialforschungsbereich 'Optimierung und Kontrolle', Bericht Nr. 117, 1997.
- 4
-
F. Bonnans,
``Second order analysis for control constrained optimal control problems
of semilinear elliptic systems'',
Applied Mathematics and Optimization, vol. 38, pp. 303-325, 1998.
- 5
-
F. Bonnans and E. Casas,
``Optimal control of semilinear multistate systems with state constraints'',
SIAM J. Control and Optimization, vol. 27, pp. 446-455, 1989.
- 6
-
F. Bonnans and E. Casas,
``An extension of Pontryagin's principle for state-constrained optimal control
problems of semilinear elliptic equations and variational inequalities'',
SIAM J. on Control and Optimization, vol. 33, pp. 274-298, 1995.
- 7
-
N. Bourbaki,
``Integration'', Chapter 9, Hermann, Paris, 1963.
- 8
-
A. Cañada, J.L. Gámez and J.A. Montero,
``Study of an optimal control problem for diffusive nonlinear elliptic
equations of logistic type'',
SIAM J. on Control and Optimization, vol. 36, pp. 1171-1189, 1998.
- 9
-
E. Casas,
``Boundary control with pointwise state constraints'',
SIAM J. Control Optim., vol. 31, pp. 993-1006, 1993
- 10
-
E. Casas, F. Tröltzsch and A. Unger,
``Second order sufficient optimality conditions for a nonlinear elliptic
control problem'',
J. for Analysis and its Applications, vol 15, pp. 687-707, 1996.
- 11
-
E. Casas, F. Tröltzsch and A. Unger,
``Second order sufficient optimality conditions for some state
constrained control problems of semilinear elliptic equations'',
Fakultät für Mathematik, Technische Universität Chemnitz,
Preprint 97-19, to appear in SIAM J. Control Optim.
- 12
-
A.R. Conn, N.I.M. Gould, and Ph.L. Toint,
LANCELOT, A Fortran Package For Large-Scale Nonlinear Optimization
(Release A),
Springer Series in Computational Mathematics, vol. 17,
(Springer Verlag, Heidelberg, 1972).
- 13
-
R. Fourer, D. M. Gay, and B. W. Kernighan,
``AMPL: A modeling Language for Mathematical Programming'',
Duxbury Press, Brooks-Cole Publishing Company, 1993
- 14
-
P.E. Gill, W. Murray, and M.A. Saunders,
SNOPT: An SQP algorithm for large-scale constrained optimization,
Report SOL 97-3, Department of EESOR, Stanford University (1997).
- 15
-
M. D. Gunzburger, L. Hou, and T. P. Svobodny,
``Finite element approximations of an optimal control problem associated with
the scalar Ginzburg-Landau equation'',
Comput. Math. Appl., vol. 21, no. 2-3, pp. 123-131, 1991.
- 16
-
M. Heinkenschloss and L. N. Vicente,
``Analysis of inexact trust-region interior-point SQP algorithms'',
TR95-18, Department of Computational and Applied Mathematics, Rice University,
1995.
- 17
-
R. Hettich, A. Kaplan and R. Tischatschke,
``Regularized penalty methods for ill-posed optimal control problems with
elliptic equations.
Part I: Distributed control with bounded control set and state constraints'',
Control and Cybernetics, vol. 26, pp. 5-27, 1997.
- 18
-
R. Hettich, A. Kaplan and R. Tischatschke,
``Regularized penalty methods for ill-posed optimal control problems with
elliptic equations.
Part II:
Distributed and boundary control with unbounded control sets and
state constraints'',
Control and Cybernetics, vol. 26, pp. 29-43, 1997.
- 19
-
K. Ito and K. Kunisch,
``Augmented Lagrangian-SQP methods for nonlinear optimal control
problems of tracking type'',
SIAM J. Optim., vol 6, pp. 96-125, 1996.
- 20
-
K. Kunisch and S. Volkwein,
``Augmented Lagrangian-SQP techniques and their approximations'',
Contemporary Mathematics, vol. 209, pp. 147-159, 1997.
- 21
-
A. Leung and S. Stojanovic,
``Optimal control for elliptic Volterra-Lotka equations'',
J. Math. Analysis and Applications, vol. 173, pp. 603-619, 1993.
- 22
-
J.L. Lions,
``Optimal control of systems governed by partial differential equations'',
Grundlehren der mathematischen Wissenschaften, Vol. 170, Springer-Verlag,
Berlin, New York, 1971.
- 23
-
H. Maurer and H.D. Mittelmann,
Optimization techniques for solving elliptic control problems with
control and state constraints. Part 1: Boundary control,
to appear in Computational Optimization and Applications.
- 24
-
H.D. Mittelmann and P. Spellucci,
``Decision Tree for Optimization Software'',
World Wide Web, http://plato.la.asu.edu/guide.html (1999).
- 25
-
H.D. Mittelmann and H. Maurer,
``Solving elliptic control problems with interior point and SQP methods:
Control and state constraints'',
to appear in the special issue ''SQP-based direct discretization methods
for practical optimal control problems'' of J. Comp. Appl. Math.,
(V. Schulz, ed.), Elsevier, 1999.
- 26
-
B.A. Murtagh and M.A. Saunders,
MINOS 5.4 User`s Guide, Report SOL 83-20R,
Department of Operations Research, Stanford University (Revised February 1995).
- 27
-
S. Rotin,
``Konvergenz des Proximal-Punkt-Verfahrens für inkorrekt gestellte
Optimalsteuerungsprobleme mit partiellen Differentialgleichungen,
Dissertation, Dept. of Mathematics, Universität Trier, Germany, 1999.
- 28
-
S. Stojanovic,
``Optimal damping control and nonlinear elliptic systems'',
SIAM J. Control Optimization, vol. 29, pp. 594-608, 1991.
- 29
-
R. S. Vanderbei and D. F. Shanno,
``An interior point algorithm for nonconvex nonlinear programming'',
to appear in Computational Optimization and Applications.
Hans D. Mittelmann
2000-10-06