Solving discretized optimization problems by partially reduced SQP methods

Computing and Visualization in Science

Volumn 1, Issue 2, 1998, Pages 83-96

  Schulz, Volker H ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

OPTIMIZATION;

APPLICATION AREA; DISCRETIZED OPTIMIZATION; NUMERICAL SOLUTION; OPTIMIZATION PROBLEMS; REDUCED SQP METHODS; SUB-PROBLEMS;

PROBLEM SOLVING;

EID: 84904997650     PISSN: 14329360     EISSN: 14330369     Source Type: Journal    
DOI: 10.1007/s007910050008     Document Type: Article

References (47)

1. U.M. Ascher, R.J. Spiteri. Collocation software for boundary value differential-algebraic equations. SIAM Journal on Scientific Computing 15(4):938-952, 1994.
2. L.T. Biegler, J. Nocedal, C. Schmid. A reduced Hessian method for large-scale constrained optimization. SIAM Journal on Optimization 5(2):314-347, 1995.
3. H.G. Bock. Numerical treatment of inverse problems in chemical reaction kinetics. In: Ebert, Deuflhard, and Jäger (eds), Modelling of Chemical Reaction Systems, volume 18 of Springer Series Chemical Physics, pages 102-125, Berlin Heidelberg New York, 1981.
4. H.G. Bock. Recent advances in parameter identification techniques for ODE. In: Deuflhard, Hairer (eds) Numerical Treatment of Inverse Problems in Differential and Integral Equations, Progress in Scientific Computing, volume 2, pages 95-121. Birkhäuser Basel, Boston, Stuttgart, 1983.
5. H.G. Bock. Randwertproblemmethoden zur Parameteridentifizierung in Systemen nichtlinearer Differentialgleichungen. Bonner Mathematische Schriften 183, Bonn, 1987.
6. H.G. Bock, E. Eich, J.P. Schlöder. Numerical solution of constrained least squares boundary value problems in differential-algebraic equations. In: Strehmel (ed), Numerical Treatment of Differential Equations. BG Teubner, Leipzig, 1988.
7. H.G. Bock, K.J. Plitt. A multiple shooting algorithm for direct solution of constrained optimal control problems. In: Proceedings 9th IFAC World Congress Automatic Control. Pergamon Press, 1984.
8. H.G. Bock, J.P. Schlöder, V.H. Schulz. Numerik großer Differentiell- Algebraischer Gleichungen - Simulation und Optimierung. In: H. Schuler (ed), Prozeßsimulation, pages 35-80. VCH Verlagsgesellschaft mbH, Weinheim, 1994.
9. H.G. Bock, J.P. Schlöder, M.C. Steinbach, H.Wörn, V.H. Schulz, R.W. Longman. Schnelle Roboter am Fließband: Mathematische Bahnoptimierung in der Praxis. In: K.-H. Hoffmann, W. Jäger, T. Lohmann, H. Schunk (eds), Mathematik - Schlüsseltechnologie für die Zukunft, pages 539-550. Springer, Berlin Heidelberg New York, 1997.
10. E.J. Cramer, J.E. Dennis, P.D. Frank, R.M. Lewis, G.R. Shubin. On alternative problem formulations for multidisciplinary design optimization. SIAM Journal on Optimization 4:754-776, 1994.
11. J.E. Dennis, M. Heinkenschloss, L.N. Vicente. Trust-region interiorpoint algorithms for a class of nonlinear programming problems. Technical Report TR94-45, Dept. Comp. Appl. Math., Rice University, Houston, TX, 1994. (to appear in SIAM J. Control and Optimization).
12. Th. Dreyer, V.H. Schulz, H.G. Bock. Entwicklung eines mathematischen Verfahrens zur schnellen Formoptimierung von Turbinenschaufeln - Abschlußbericht zum AG-Turbo Projekt 1.110. Technical report, IWR, Universität Heidelberg, 1995.
13. R. Fletcher. Practical Methods of Optimization. John Wiley and Sons, New York, 1987.
14. R. Fontecilla. On inexact quasi-Newton methods for constrained optimization. In: P.T. Boggs, R.H. Byrd, R.B. Schnabel (eds), Numerical Optimization 1984, pages 102-118. SIAM, Philadelphia, 1985.
15. P.D. Frank, G.R. Shubin. A comparison of optimization-based approaches for a model computational aerodynamics design problem. J. Comput. Physics 98:74-89, 1992.
16. G. Fritsch. Berechnung der zweidimensionalen Umfangslösung entlang einer beliebigen Rotationsstromfläche erster Art mit Hilfe eines Stromfunktionsverfahrens in konservativer Formulierung. Master's thesis, Universität Stuttgart, 1987.
17. D. Gabay. Reduced quasi-Newton methods with feasibility improvement for nonlinear constrained optimization. Mathematical Programming Study 16:18-44, 1982.
18. P.E. Gill, W. Murray, M.H. Wright. Practical optimization. Academic Press, London, 1981.
19. C.B. Gurwitz, M.L. Overton. Sequential quadratic programming methods based on approximating a projected Hessian matrix. SIAM Journal on Scientific and Statistical Computing 10(4):631-635, 1989.
20. W. Hackbusch. Multigrid methods and applications. Springer, Berlin Heidelberg New York 1985.
21. R.T. Haftka, Z. Gurdal, M.P. Kamat. Elements of structural optimization. Kluwer Academic Publishers, Norwell, MA, 1990.
22. S.-P. Han. Superlinearly convergent variable metric algorithms for general nonlinear programming problems. Mathematical Programming 11:263-282, 1976.
23. S.-P. Han. A globally convergent method for nonlinear programming. Journal of Optimization Theory and Applications 22:297-309, 1977.
24. M. Heinkenschloss. Projected sequential quadratic programming methods. SIAM Journal on Optimization 6:373-417, 1996.
25. J. Konzelmann, H.G. Bock, R.W. Longman. Time optimal trajectories of elbow robots by direct methods. In: Proceedings of the 1989 AIAA Guidance, Navigation and Control Conference, Boston, volume 2, pages 895-910, 1989.
26. J. Konzelmann, H.G. Bock, R.W. Longman. Time optimal trajectories of polar robot manipulators by direct methods. Modeling and Simulation, Instrument Society of America 20(5):1933-1939, 1989.
27. F.-S. Kupfer, E.W. Sachs. Reduced SQP methods for nonlinear heat conduction control problems. International Series of Numerical Mathematics 111:145-160, 1993.
28. R.W. Longman. The kinetics and workspace of a satellite-mounted robot. The Journal of the Astronautical Sciences, Special Issue on Robotics in Space 38(4):423-440, 1990. Conference version appeared in The Proceedings of the 1988 AIAA Guidance, Navigation and Control Conference, Minneapolis, Minnesota, pp. 374-381.
29. R.W. Longman, H.G. Bock, V.H. Schulz. Path planning for satellite mounted robots. In: C.L. Kirk, D.J. Inman (eds), Dynamics and control of structures in space III, volume 1, pages 707-716. Computational Mechanics Publication, Southampton, Boston, 1996.
30. J. Nocedal, M.L. Overton. Projected Hessian updating algorithms for nonlinearly constrained optimization. SIAM Journal on Numerical Analysis 22(5):821-850, 1985. (Pubitemid 15559633)
31. M.J.D. Powell. A fast algorithm for nonlinearly constrained optimization calculations. In: G.A. Watson (ed), Numerical Analysis Proceedings Dundee 1977, pages 144-157. Springer, Berlin Heidelberg New York, 1978.
32. V.H. Schulz. A direct PRSQP method for path planning of satellite mounted robots. Zeitschrift für angewandte Mathematik und Mechanik 76(S3):17-20, 1996.
33. V.H. Schulz. Numerical optimization of the cross-sectional shape of turbine blades. Zeitschrift für angewandte Mathematik und Mechanik 76(S1):207-210, 1996. (Pubitemid 126110560)
34. V.H. Schulz. Optimal paths for satellite mounted robots. Zeitschrift für angewandte Mathematik und Mechanik 76(S3):291-294, 1996.
35. V.H. Schulz. Reduced SQP methods for large-scale optimal control problems in DAE with application to path planning problems for satellite mounted robots. PhD thesis, Universität Heidelberg, 1996.
36. V.H. Schulz, H.G. Bock, R.W. Longman. Optimal path planning for satellite mounted robot manipulators. Advances in the Astronautical Sciences 82:311-329, 1993. (Pubitemid 23712679)
37. V.H. Schulz, H.G. Bock, R.W. Longman. Shortest paths for satellite mounted robot manipulators. International Series of Numerical Mathematics 115:357-366, 1994.
38. V.H. Schulz, H.G. Bock, M.C. Steinbach. Exploiting invariants in the numerical solution of multipoint boundary value problems in DAE. SIAM Journal on Scientific Computing 19(2), 1998.
39. V.H. Schulz, Th. Dreyer, Th. Speer, H.G. Bock. Optimum shape design of turbine blades. In: P. Kleinschmidt, A. Bachem, U. Derigs, D. Fischer, U. Leopold-Wildburger, and R. Möhring (eds), Operations Research Proceedings 1995, pages 190-195. Springer, Berlin Heidelberg New York, 1996.
40. V.H. Schulz, R.W. Longman, H.G. Bock. Computer-aided motion planning for satellite mounted robots. Mathematical Methods in the Applied Sciences, 1997. (to appear).
41. M. Steinbach, H.G. Bock, R.W. Longman. Time optimal extension or retraction in polar coordinate robots: Numerical analysis of the switching structure. Journal of Optimization Theory and Applications 84(3):589-616, 1995.
42. M.C. Steinbach. Fast recursive SQP methods for large-scale optimal control problems. PhD thesis, Universität Heidelberg, 1995.
43. M.C. Steinbach. Structured interior point SQP methods in optimal control. Zeitschrift für angewandte Mathematik und Mechanik 76(S3):59- 62, 1996.
44. S. Ta'Asan, G. Kuruvila, M.D. Salas. Aerodynamic design and optimization in one shot. In: 30th Aerospace Sciences Meeting, Reno, NV, number AIAA Paper 92-0025, 1992.
45. R.A. Tapia. On secant updates for use in general constrained optimization. Mathematics of Computation 51:181-202, 1988.
46. I.-B. Tjoa, L. Biegler. Simultaneous solution and optimization strategies for parameter estimation of differential-algebraic systems. Ind. Eng. Chem. Res. 30(2):376-385, 1991.
47. Ch. Wu. A general theory of the three-dimensional flow in subsonic and supersonic turbomachines of axial, radial, and mixed flow type. Technical report, NACA TN 2604, 1952.