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Object Library of Algorithms for Dynamic Optimization Problems: Benchmarking SQP and Nonlinear Interior Point Methods Cover

Object Library of Algorithms for Dynamic Optimization Problems: Benchmarking SQP and Nonlinear Interior Point Methods

Open Access
|Jan 2008

References

  1. Arnold E. and Puta H. (1994): An SQP-type solution method for constrained discrete-time optimal control problems. In: Computational Optimal Control (R. Bulirsch and D. Kraft, Eds.), Birkhäuser Verlag, Basel, Switzerland, pp. 127-136.10.1007/978-3-0348-8497-6_11
  2. Arnold E., Tatjewski P. and Wołochowicz P. (1994): Two methods for large-scale nonlinear optimization and their comparison on a case study of hydropower optimization.Journal of Optimization Theory and Applications, Vol. 81, No. 2, pp. 221-248.10.1007/BF02191662
  3. Benson H. Y., Shanno D. F. and Vanderbei R. J. (2001): Interior-point methods for nonconvex nonlinear programming: Filter methods and merit functions. Technical Report ORFE-00-06, Operations Research and Financial Engineering, Princeton University. Available at http://www.princeton.edu/~rvdb/tex/loqo4/loqo4_4.pdf
  4. Benson H. Y., Shanno D. F. and Vanderbei R. J. (2002): A comparative study of large-scale nonlinear optimization algorithms. Technical Report ORFE-01-04, Operations Research and Financial Engineering, Princeton University. Available at http://www.princeton.edu/~rvdb/tex/loqo5/loqo5_5.pdf
  5. Bertsekas D. P. (1982): Projected Newton methods for optimization problems with simple constraints.SIAM Journal on Control and Optimization, Vol. 20, No. 2, pp. 221-246.10.1137/0320018
  6. Błaszczyk J., Karbowski A. and Malinowski K. (2002a): Object library of algorithms for unconstrained dynamic optimization problems. Proceedings of the 14-th National Conference on Automatic Control (KKA), Vol. I, Zielona Góra, Poland, pp. 451-456.
  7. Błaszczyk J., Karbowski A. and Malinowski K. (2002b): Object library of algorithms for dynamic optimization problems without constraints or with simple bounds on control. Proceedings of the 8th IEEE International Conference on Methods and Models in Automation and Robotics, Vol. 1, Szczecin, Poland, pp. 257-262.
  8. Błaszczyk J., Karbowski A. and Malinowski K. (2003): Object library of algorithms for dynamic optimization problems with general constraints. Proceedings of the 9th IEEE International Conference on Methods and Models in Automation and Robotics, Vol. 1, Międzyzdroje, Poland, pp. 271-276.
  9. Bryson A. E. (1998): Dynamic Optimization. Menlo Park CA: Addison-Wesley, p. 550.
  10. Byrd R. H., Hribar M. E. and J. Nocedal (1999): An interior point algorithm for large scale nonlinear programming.SIAM Journal on Optimization, Vol. 9, No. 4, pp. 877-900.
  11. Byrd R. H., Gilbert J. Ch. and Nocedal J. (2000): A trust region method based on interior point techniques for nonlinear programming.Mathematical Programming, Vol. 89, pp. 149-185.10.1007/PL00011391
  12. Chamberlain R. M., Powell M. J. D., Lemarechal C. and Pedersen H. C. (1982): The watchdog technique for forcing convergence in algorithms for constrained optimization.Mathematical Programming Study, Vol. 16, pp. 1-17.10.1007/BFb0120945
  13. Dolan E. D. and Moré J. J. (2002): Benchmarking optimization software with performance profiles.Mathematical Programming, Vol. 91, No. 2, pp. 201-213.10.1007/s101070100263
  14. Fiacco A. V. and McCormick G. P. (1968): Nonlinear Programming: Sequential Unconstrained Minimization Techniques. John Wiley and Sons, New York/London.
  15. Findeisen W., Szymanowski J. and Wierzbicki A. (1980): Theory and Computational Methods of Optimization. Polish Scientific Publishers, Warsaw (in Polish).
  16. Fletcher R. (1987): Practical Methods of Optimization. John Wiley and Sons, New York, NY, USA.
  17. Fletcher R. (1995): An optimal positive definite update for sparse Hessian matrices.SIAM Journal on Optimization, Vol. 5, No. 1, pp. 192-218.10.1137/0805010
  18. Fletcher R. and Leyffer S. (2002): Nonlinear programming without a penalty function.Mathematical Programming, Vol. 91, No. 2, pp. 239-269.10.1007/s101070100244
  19. Fletcher R., Leyffer S. and Toint Ph. L. (2006): A brief history of filter methods. Technical Report ANL/MCS-P1372-0906, Mathematics and Computer Science Division, Argonne National Laboratory. Available at http://www.optimization-online.org/DB_FILE/2006/10/1489.pdf
  20. Franke R. (1994): Anwendung von Interior-Point-Methoden zur Lösung zeitdiskreter Optimalsteuerungsprobleme. M.S. thesis, Techniche Universität Ilmenau, Fakultät für Informatik und Automatsierung, Institut für Automatisierungsund Systemtechnik Fachgebiet Dynamik und Simulation ökologischer Systeme, Ilmenau, Germany, (in German).
  21. Franke R. (1998): OMUSES -A tool for the optimization of multistage systems and HQP - A solver for sparse nonlinear optimization. Version 1.5. Department of Automation and Systems Engineering, Technical University of Ilmenau, Germany. Available at ftp://ftp.systemtechnik.tu-ilmenau.de/pub/reports/omuses.ps.gz
  22. Franke R. and Arnold E. (1997): Applying new numerical algorithms to the solution of discrete-time optimal control problems. In: Computer-Intensive Methods in Control and Signal Processing: The Curse of Dimensionality, (Warwick K. and Kárný M., Eds.), Birkhäuser Verlag, Basel, Switzerland, pp. 105-118.10.1007/978-1-4612-1996-5_6
  23. The solver Omuses/HQP for structured large-scale constrained optimization: Algorithm, implementation, and example application. Proceedings of the 6-th SIAM Conference on Optimization, Atlanta.
  24. Goldfarb D. and Idnani A. (1983): A numerically stable dual method for solving strictly convex quadratic programs.Mathematical Programming, Vol. 27, No. 1, pp. 1-33.10.1007/BF02591962
  25. Gondzio J. (1994): Multiple centrality corrections in a primal-dual method for linear programming. Technical Report. 20, Department of Management Studies, University of Geneva, Geneva, Switzerland. Available at http://www.maths.ed.ac.uk/~gondzio/software/correctors.ps
  26. Griewank A., Juedes D., Mitev H., Utke J., Vogel O. and Walther A. (1999): ADOL-C: A package for the automatic differentiation of algorithms written in C/C++, Version 1.8.2, March 1999. Available at http://www.math.tu-dresden.de/~adol-c/
  27. Karmarkar N. (1984): A new polynomial-time algorithm for linear programming.Combinatorica, Vol. 4, No. 4, pp. 373-395.10.1007/BF02579150
  28. Luus R. (2000): Iterative Dynamic Programming. CRC Press, Inc., Boca Raton, FL, USA.
  29. Mehrotra S. (1992): On the implementation of a primal-dual interior point method.SIAM Journal on Optimization, Vol. 2, No. 4, pp. 575-601.10.1137/0802028
  30. Misc J.-P. (2003): Large scale nonconvex optimization.SIAM's SIAG/OPT Newsletter Views-and-News, Vol. 14, No. 1, pp. 1-25. Available at http://fewcal.uvt.nl/sturm/siagopt/vn14_1.pdf
  31. Morales J. L., Nocedal J., Waltz R. A., Liu G. and Goux J.-P. (2001): Assessing the potential of interior methods for nonlinear optimization. Technical Report OTC 2001/4, Optimization Technology Center of Northwestern University. Available at http://www.ece.northwestern.edu/~morales/PSfiles/assess.ps
  32. Nocedal J. and Wright S. J. (1999): Numerical Optimization. Berlin: Springer-Verlag.10.1007/b98874
  33. De O. Pantoja J. F.A. (1988): Differential dynamic programming and Newton's method.International Journal of Control, Vol. 47, No. 5, pp. 1539-1553.10.1080/00207178808906114
  34. Powell M. J. D. (1978): A fast algorithm for nonlinearly constrained optimization calculations. In: Numerical Analysis, Dundee (G. A. Watson, Ed.), Dundee: Springer-Verlag, pp. 144-157.10.1007/BFb0067703
  35. Powell M. J. D. (1985): On the quadratic programming algorithm of Goldfarb and Idnani.Mathematical Programming Study, Vol. 25, pp. 46-61.10.1007/BFb0121074
  36. Salahi M., Peng J. and Terlaky T. (2005): On Mehrotratype predictor-corrector algorithms. Technical report, Advanced Optimization Lab, Department of Computing and Software, McMaster University, Hamilton, Ontario, Canada. Available at http://www.optimization-online.org/DB_FILE/2005/03/1104.pdf
  37. Schittkowski K. (1980): Nonlinear Programming Codes: Information, Tests, Performance. Berlin: Springer-Verlag.10.1007/978-3-642-46424-9
  38. Schittkowski K. (1983): On the convergence of a sequential quadratic programming method with an augmented Lagrangian line search function. Mathematishe Operations Forschung und Statistik, Ser. Optimization, Vol. 14, No. 2, pp. 197-216.10.1080/02331938308842847
  39. Schwartz A. and Polak E. (1997): Family of projected descent methods for optimization problems with simple bounds.Journal of Optimization Theory and Applications, Vol. 92, No. 1, pp. 1-31.10.1023/A:1022690711754
  40. Tenny M. J., Wright S. J. and Rawlings J. B. (2002): Nonlinear model predictive control via feasibility-perturbed sequential quadratic programming. Technical Report TWMCC-2002-02, Texas-Wisconsin Modeling and Control Consortium. Available at http://jbrwww.che.wisc.edu/jbr-group/tech-reports/twmcc-2002-02.pdf
  41. Tits A. L., Wächter A., Bakhtiari S., Urban T. J. and Lawrence C.T. (2002): A primal-dual interior-point method for nonlinear programming with strong global and local convergence properties. Technical Report TR 2002-29, Institute for Systems Research, University of Maryland. Available at http://www.ee.umd.edu/~andre/pdiprev.ps
  42. Ulbrich M., Ulbrich S. and Vicente L. N. (2004): A globally convergent primal-dual interior-point filter method for nonlinear programming.Mathematical Programming, Vol. 100, No. 2, pp. 379-410.10.1007/s10107-003-0477-4
  43. Vanderbei R. J. and Shanno D. F. (1997): An interior-point algorithm for non-convex nonlinear programming. Technical Report SOR-97-21, Statistics and Operations Research, Princeton University. Available at http://www.sor.princeton.edu/~rvdb/ps/nonlin.ps.gz
  44. Wächter A. (2002): An Interior Point Algorithm for Large-Scale Nonlinear Optimization with Applications in Process Engineering. Ph.D. dissertation, Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA, USA. Available at http://www.research.ibm.com/people/a/andreasw/papers/thesis.pdf
  45. Wächter A. and Biegler L. T. (2000): Failure of global convergence for a class of interior point methods for nonlinear programming.Mathematical Programming, Vol. 88, No. 3, pp. 565-574.10.1007/PL00011386
  46. Wächter A. and Biegler L. T. (2005): Line search filter methods for nonlinear programming: Motivation and global convergence.SIAM Journal on Optimization, Vol. 16, No. 1, pp. 1-31.10.1137/S1052623403426556
  47. Wächter A. and Biegler L. T. (2006): On the implementation of a primal-dual interior-point filter line-search algorithm for large-scale nonlinear programming.Mathematical Programming, Vol. 106, No. 1, pp. 25-57.10.1007/s10107-004-0559-y
  48. Waltz R. A. and Plantenga T. (2006): KNITRO 5.0 User's Manual. Available at http://www.ziena.com/docs/knitroman.pdf
  49. Wierzbicki A. (1984): Models and Sensitivity of Control Systems. Elsevier, Amsterdam.
  50. Wright S. J. (1993): Interior point methods for optimal control of discrete time systems.Journal of Optimization Theory and Applications, Vol. 77, No. 1, pp. 161-187.10.1007/BF00940784
  51. Wright S. J. (1997): Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA.10.1137/1.9781611971453
  52. Yakowitz S. and Rutherford B. (1984): Computational aspects of discrete-time optimal control.Applied Mathematics and Computation, Vol. 15, No. 1, pp. 29-45.10.1016/0096-3003(84)90051-1
DOI: https://doi.org/10.2478/v10006-007-0043-y | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Language: English
Page range: 515 - 537
Published on: Jan 7, 2008
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2008 Jacek Błaszczyk, Andrzej Karbowski, Krzysztof Malinowski, published by University of Zielona Góra
This work is licensed under the Creative Commons License.

Volume 17 (2007): Issue 4 (December 2007)