On minimizing quadratically constrained ratio of two quadratic functions

Journal of Convex Analysis

Volumn 17, Issue 3-4, 2010, Pages 789-804

  Beck, Amir ^a   Teboulle, Marc ^b  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 78149297923     PISSN: 09446532     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (26)

1. A. Auslender: How to deal with the unbounded in optimization: theory and algorithms. Math. Program., Ser. A 79 (1997) 3-18.
2. A. Auslender, M. Teboulle: Asymptotic Cones and Functions in Optimization and Variational Inequalities, Springer, New York, 2003.
3. A. Beck: Quadratic matrix programming, SIAM J. Optim. 17(4) (2006) 1224-1238.
4. A. Beck, A. Ben-Tal: On the solution of the Tikhonov regularization of the total least squares problem, SIAM J. Optim. 17(1) (2006) 98-118.
5. A. Beck, A. Ben-Tal, M. Teboulle: Finding a global optimal solution for a quadratically constrained fractional quadratic problem with applications to the regularized total least squares, SIAM J. Matrix Anal. Appl. 28(2) (2006) 425-445.
6. A. Beck, M. Teboulle: A convex optimization approach for minimizing the ratio of indefinite quadratic functions over an ellipsoid, Math. Program., Ser. A 118(1) (2009) 13-35.
7. A. Ben-Tal, A. Nemirovski: Lectures on Modern Convex Optimization, MPS/SIAM Series on Optimization, SIAM, Philadelphia (2001).
8. A. Ben-Tal, M. Teboulle: Hidden convexity in some nonconvex quadratically constrained quadratic programming, Math. Program., Ser. A 72(1) (1996) 51-63.
9. W. Dinkelbach: On nonlinear fractional programming, Manage. Sci., Ser. A 13 (1967) 492-498.
10. R. D. Fierro, G. H. Golub, P. C. Hansen, D. P. O'Leary: Regularization by truncated total least squares, SIAM J. Sci. Comput. 18(1) (1997) 1223-1241.
11. G. H. Golub, P. C. Hansen, D. P. O'Leary: Tikhonov regularization and total least squares, SIAM J. Matrix Anal. Appl. 21(2) (1999) 185-194.
12. G. H. Golub, C. F. Van Loan: An analysis of the total least-squares problem, SIAM J. Numer. Anal. 17(6) (1980) 883-893.
13. G. H. Golub, C. F. Van Loan: Matrix Computations. 3rd Ed., Johns Hopkins Univ. Press, Baltimore (1996).
14. H. Guo, R. Renaut: A regularized total least squares algorithm, in: Total Least Squares and Errors-in-Variables Modeling. Analysis, Algorithms and Applications, S. Van Huffel, P. Lemmerling (eds.), Kluwer, Dordrecht (2002) 57-66.
15. P. C. Hansen: The use of the L-curve in the regularization of discrete ill-posed problems, SIAM J. Sci. Comput. 14 (1993) 1487-1503.
16. P. C. Hansen: Regularization tools, a matlab package for analysis of discrete regularization problems, Numer. Algorithms 6 (1994) 1-35.
17. P. C. Hansen: Rank-Deficient and Discrete Ill-Posed Problems. Numerical Aspects of Linear Inversion, SIAM, Philadelphia (1998).
18. R. A. Horn, C. R. Johnson: Matrix Analysis, Cambridge Univ. Press, Cambridge (1985).
19. R. Horst, P. M. Pardalos (eds.): Handbook of Global Optimization, Kluwer, Dordrecht (1995).
20. S. Van Huffel, J. Vandewalle: The Total Least-Squares Problem: Computational Aspects and Analysis, Frontier in Applied Mathematics 9, SIAM, Philadelphia (1991).
21. Y. Nesterov, A. Nemirovski: Interior-Point Polynomial Algorithms in Convex Programming, SIAM, Philadelphia (1994).
22. G. Pataki: The geometry of semidefinite programming, in: Handbook of Semidefinite Programming. Theory, Algorithms, and Applications, H. Wolkowicz et al. (ed.), Int. Ser. Oper. Res. Manag. Sci. 27, Kluwer, Boston (2000) 29-65.
23. D. Sima, S. Van Huffel, G. H. Golub: Regularized total least squares based on quadratic eigenvalue problem solvers, BIT 44(4) (2004) 793-812.
24. J. F. Sturm: Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones, Optim. Methods Softw. (11-12) (1999) 625-653.
25. L. Vandenberghe, S. Boyd: Semidefinite programming, SIAM Rev. 38(1) (1996) 40-95.
26. F. Zhang: Matrix Theory: Basic Results and Techniques, Universitext, Springer, New York (1999).