On the numerical solution of bound constrained optimization problems

Ana Friedlander; José Mario Martínez

RAIRO - Operations Research - Recherche Opérationnelle (1989)

  • Volume: 23, Issue: 4, page 319-341
  • ISSN: 0399-0559

How to cite


Friedlander, Ana, and Martínez, José Mario. "On the numerical solution of bound constrained optimization problems." RAIRO - Operations Research - Recherche Opérationnelle 23.4 (1989): 319-341. <http://eudml.org/doc/104967>.

author = {Friedlander, Ana, Martínez, José Mario},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {differentiable concave function; active set strategies; global convergence},
language = {eng},
number = {4},
pages = {319-341},
publisher = {EDP-Sciences},
title = {On the numerical solution of bound constrained optimization problems},
url = {http://eudml.org/doc/104967},
volume = {23},
year = {1989},

AU - Friedlander, Ana
AU - Martínez, José Mario
TI - On the numerical solution of bound constrained optimization problems
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 1989
PB - EDP-Sciences
VL - 23
IS - 4
SP - 319
EP - 341
LA - eng
KW - differentiable concave function; active set strategies; global convergence
UR - http://eudml.org/doc/104967
ER -


  1. 1. D. P. BERTSEKAS, Projected Newton Methods for Optimization problems with simple constraints, SIAM J. Control Optim., Vol. 20, 1982, pp. 221-246. Zbl0507.49018MR646950
  2. 2. M. J. BEST and K. RITTER, An Effective Algorithm for Quadratic Minimization Problems, MRC Tech. Rep. 1691, Mathematîcs Research Center, University of Wisconsin-Madison, 1976. 
  3. 3. A. BJORCK, A Direct Method for Sparse Least-Squares Problems with Lower and Upper Bounds, Department of Mathematics, Linkoping University, Linkoping, Sweden, 1987. Zbl0659.65039
  4. 4. P. H. CALAMAI and J. J. MORÉ, Projected Gradient Methods for Linearly Constrained Problems, Mathematical Programming, Vol. 39, 1987, pp. 93-116. Zbl0634.90064MR909010
  5. 5. J. CEA and R. GLOWINSKI, Sur des méthodes d'optimisation par relaxation, RAIRO R-3, 1953, pp. 5-32. Zbl0279.90033
  6. 6. A. K. CLINE, C. B. MOLER, G. W. STEWART and J. H. WILKINSON, An Estimate of the Condition Number of a Matrix, SIAM J. Numer. Anal., Vol. 16, 1979, pp. 368-375. Zbl0403.65012MR526498
  7. 7. R. S. DEMBO and U. TULOWITZKI, On the Minimization of Quadratic Functions Subject to Box Constraints, Working paper series B 71, School of Organization and Management, Yale University, New Haven, 1987. 
  8. 8. J. E. DENNIS and R. S. SCHNABEL, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice Hall, NJ, 1983. Zbl0579.65058MR702023
  9. 9. R. FLETCHER and C. M. REEVES, Function Minimization by Conjugate Gradients, Computer J., Vol. 2, 1964, pp. 149-153. Zbl0132.11701MR187375
  10. 10. P. E. GILL and W. MURRAY, Minimization Subject to Bounds on the Variables, NPL report NAC 72, National Physical Laboratory, Teddington, 1976. 
  11. 11. P. E. GILL and W. MURRAY, Numerically Stable Methods for Quadratic Programming, Mathematical Programming, Vol. 14, 1978, pp. 349-372. Zbl0374.90054MR484411
  12. 12. P. E. GILL, W. MURRAY, M. A. SAUNDERS and M. WRIGHT, A Note on Nonlinear Approaches to Linear Programmong, TR SOL 86-7, Systems Optimization Labotory, Stanford University, Stanford, 1986. 
  13. 13. P. E. GILL, W. MURRAY and M. WRIGHT, Practical Optimization, Academic Press, London-New York, 1981. Zbl0503.90062MR634376
  14. 14. G. H. GOLUB and C. F. VAN LOAN, Matrix Computations, The John Hopkins University Press, Baltimore, 1983. Zbl0733.65016MR733103
  15. 15. G. T. HERMAN, Image Reconstruction from Projections: The Fundamentals of Computerized Tomography. Academic Press, New York, 1980. Zbl0538.92005MR630896
  16. 16. N. KARMARKAR, A New Polynomial-Time Algorithm for Linear Programming, Combinatorica, Vol. 4, 1984, pp. 373-395. Zbl0557.90065MR779900
  17. 17. P. LÖTSTEDT, Solving the Minimal Least Squares Problem Subject to Bounds on the Variables, BIT, Vol. 24, 1984, pp. 206-224 Zbl0546.65041MR753549
  18. 18. J. J. MORÉ, Numerical Solution of Bound Constrained Problems, ANL/MCS-TM-96, Math. and Comp. Sci. Div., Argonne National Laboratory, Argonne, Illinois, 1987. Zbl0655.65086MR951428
  19. 19. D. P. O'LEARY, A Generalized Conjugate Gradient Algorithm for Solving a Class of Quadratic Programming Problems, Linear Algebra and its Applications, Vol.34, 1980, pp. 371-399. Zbl0464.65039MR591439
  20. 20. M. J. D. POWELL, Subroutine GSRCH, Harwell Subroutine Library, Harwell, Oxfordshire, 1980. 
  21. 21. B. T. POLYAK, The Conjugate Gradient Method in Extremal Problems, USSR Computational Mathematics and Mathematical Physics, Vol. 9, 1969, pp. 94-112. Zbl0229.49023

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.