A reduced Newton method for constrained linear least-squares problems

Journal of Computational and Applied Mathematics

Volumn 233, Issue 9, 2010, Pages 2200-2212

  Morini, Benedetta ^a   Porcelli, Margherita ^a   Chan, Raymond H ^b  

^a UNIVERSITY OF FLORENCE   (Italy)

^b CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Active set strategy; Bound constrained linear least squares problems; Image processing; Newton method

Indexed keywords

ACTIVE SETS; BOUND-CONSTRAINED LINEAR LEAST-SQUARES PROBLEMS; DYNAMIC RANGE; IMAGE DEBLURRING; LINEAR LEAST SQUARES; NEWTON METHODS;

IMAGE PROCESSING; IMAGING SYSTEMS; LINEAR SYSTEMS; NONLINEAR EQUATIONS; NONLINEAR SYSTEMS; QUADRATIC PROGRAMMING;

NEWTON-RAPHSON METHOD;

EID: 73249124320     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2009.10.006     Document Type: Article

References (24)

1. Björck A. Numerical Methods for Least Squares Problems (1996), SIAM
2. Ehrgott M., and Winz I. Interactive decision support in radiation therapy treatment planning. OR Spectrum 30 (2008) 311-329
3. Gonzalez R., and Woods R. Digital Image Processing. 3rd ed. (2008), Prentice Hall, NJ
4. Ng M. Iterative Methods for Toeplitz Systems (2004), Oxford University Press, Oxford
5. Rudin L., Osher S., and Fatemi E. Nonlinear total variation based noise removal algorithms. Physica D 60 (1992) 259-268
6. Huang Y., Ng M., and Wen Y. A fast total variation minimization method for image restoration. SIAM Journal on Multiscale Modeling and Simulation 7 (2008) 774-795
7. Bellavia S., Gondzio J., and Morini B. Regularization and preconditioning of KKT systems arising in nonnegative least-squares problems. Numerical Linear Algebra with Applications 16 (2009) 39-61
8. S. Bellavia, J. Gondzio, B. Morini, Computational experience with numerical methods for nonnegative least-squares problems, Report 09/04, Dipartimento di Energetica S. Stecco, Università di Firenze, (submitted for publication)
9. Bellavia S., Macconi M., and Morini B. An interior Newton-like method for nonnegative least-squares problems with degenerate solution. Numerical Linear Algebra with Applications 13 (2006) 825-846
10. D. Chen, R. Plemmons, Nonnegativity constraints in numerical analysis, in: A. Bultheel, R. Cools (Eds.) Conference Proceedings of the Symposium on the Birth of Numerical Analysis, Leuven Belgium, October 2007, World Scientific Press, 2009, (in press)
11. Friedlander M., and Hatz K. Computing nonnegative tensor factorizations. Optimization Methods and Software 23 (2008) 631-647
12. Hager W., Mair B., and Zhang H. An Affine-scaling interior-point CBB method for box-constrained optimization. Mathematical Programming 119 (2009) 1-32
13. B. Kim, Numerical optimization methods for image restoration. Ph.D. Thesis, Stanford University, 2002
14. Morigi S., Reichel L., Sgallari F., and Zama F. An iterative method for linear discrete ill-posed problems with box constraints. Journal of Computational and Applied Mathematics 198 (2007) 505-520
15. Coleman T., and Li Y. An interior trust-region approach for nonlinear minimization subject to bounds. SIAM Journal on Optimization 6 (1996) 418-445
16. Heinkenschloss M., Ulbrich M., and Ulbrich S. Superlinear and quadratic convergence of affine-scaling interior-point Newton methods for problems with simple bounds without strict complementarity assumptions. Mathematical Programming (1999)
17. Kanzow C. An active set-type Newton method for constrained nonlinear systems. In: Ferris M.C., Mangasarian O.L., and Pang J.S. (Eds). Complementarity: Applications, Algorithms and Extensions (2001), Kluwer Academic Publishers 179-200
18. Golub G., and Van Loan C. Matrix Computations. 3rd ed. (1996), The Johns Hopkins University Press, London
19. Kanzow C., and Klug A. On affine-scaling interior-point Newton methods for nonlinear minimization with bound constraints. Computational Optimization and Applications 35 (2006) 177-197
20. Conn A., Gould N., and Toint P. Trust-region methods. SMPS/SIAM Series on Optimization (2000)
21. Berkeley Segmentation Dataset: Images, http://www.eecs.berkeley.edu/Research/Projects/CSvision/grouping/segbench/BSDS300/html/dataset/images.html
22. Ng M., Chan R., and Tang W. A fast algorithm for deblurring models with Neumann boundary conditions. SIAM Journal on Scientific Computing 21 (2000) 851-866
23. Chan R.H., and Jin X.Q. An introduction to iterative Toeplitz solvers. Fundamentals of Algorithms (2007), SIAM
24. Bovik A. Handbook of Image and Video Processing (2000), Academic Press