Convex feasibility problem with prioritized hard constraints - Double layered projected gradient method

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

Volumn E87-A, Issue 4, 2004, Pages 872-878

  Ogura, Nobuhiko ^a   Yamada, Isao ^a  

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

Convex feasibility problem; Convex projection; Fixed point theorem; Hard constraint; Nonexpansive mapping

Indexed keywords

ALGORITHMS; ASYMPTOTIC STABILITY; BANDWIDTH; COMPUTER SIMULATION; FOURIER TRANSFORMS; INFORMATION ANALYSIS; MAPPING; PROBLEM SOLVING; SET THEORY; SPECTRUM ANALYSIS;

CONVEX FEASIBILITY PROBLEM; CONVEX PROJECTION; FIXED POINT THEOREM; HARD CONSTRAINT; NONEXPANSIVE MAPPING;

IMAGE PROCESSING;

EID: 2342459111     PISSN: 09168508     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (31)

1. J.B. Baillon, R.E. Bruck, and S. Reich, "On the asymptotic behavior of nonexpansive mappings and semigroups in Banach spaces," Houston J. Math., vol.4, pp. 1-9, 1978.
2. H.H. Bauschke and J.M. Borwein, "On projection algorithms for solving convex feasibility problems," SIAM Review, vol.38, no.3, pp.367-426, Sept. 1996.
3. H.H. Bauschke, J.M. Borwein, and A.S. Lewis, "The method of cyclic projections for closed convex sets in Hilbert space," Contemporary Math., vol.204, pp.1-38, 1997.
4. M.G. Bellanger, Adaptive Digital Filters and Signal Analysis, Marcel Dekker, New York, 1987.
5. Y. Censor, A.N. Iusem, and S.A. Zenios, "An interior point method with Bregman functions for the variational inequality problem with paramonotone operators," Math. Programming, vol.81, pp.373-400, 1998.
6. M.R. Civanlar and R.A. Nobakht, "Optimal pulse shape design using projections onto convex sets," Proc. Int. Conf. Acoust., Speech Signal Process., pp. 1874-1877, 1988.
7. P.L. Combettes, "Foundation of set theoretic estimation," Proc. IEEE, vol.81, no.2, pp.182-208, 1993.
8. P.L. Combettes, "Inconsistent signal feasibility problems: Least-squares solution in a product space," IEEE Trans. Signal Process., vol.42, no.11, pp.2955-2966, Nov. 1994.
9. P.L. Combettes and P. Bondon, "Hard-constrained inconsistent signal feasibility problems," IEEE Trans. Signal Process., vol.47, no.9, pp.2460-2468, 1999.
10. F. Deutsch and I. Yamada, "Minimizing certain convex functions over the intersection of the fixed point sets of nonexpansive mappings," Numer. Funct. Anal. Optim., vol.19, nos.1&2, pp.33-56, 1998.
11. K. Dostert, Power Line Communications, Pearson Education, 2001.
12. M. Goldburg and R.J. Marks, II, "Signal synthesis in the presence of an inconsistent set of constraints," IEEE Trans. Circuits Syst., vol.32, no.7, pp.647-663, 1985.
13. E.G. Golshtein and N.V. Tretyakov, Modified Lagrangians & Monotone Maps in Optimization, Wiley, 1996.
14. A.A. Goldstein, "Convex programming in Hilbert space," Bull. Amer. Math. Soc., vol.70, pp.709-710, 1964.
15. H. Hasegawa, I. Yamada, and K. Sakaniwa, "A design of near perfect reconstruction linear-phase QMF banks based on hybrid steepest descent method," IEICE Trans. Fundamentals, vol.E83-A, no.8, pp.1523-1530, Aug. 2000.
16. S. Haykin, Communication Systems, 4th ed., John Wiley & Sons, New York, 2001.
17. E.S. Levitin and B.T. Polyak, "Constrained minimization method," USSR Computational Mathematics and Mathematical Physics, vol.6, pp.1-50, 1966.
18. F. Liu and M.Z. Nashed, "Regularization of nonlinear ill-posed variational inequalities and convergence rates," Set-Valued Analysis, vol.6, pp.313-344, 1998.
19. R.W. Lucky, J. Salz, and E.J. Weldon, Jr., Principles of data communication, McGraw-Hill, 1968.
20. N. Ogura and I. Yamada, "Non-strictly convex minimization over the fixed point set of an asymptotically shrinking nonexpansive mapping," Numer. Funct. Anal. Optim., vol.23, nos.1&2, pp.113-137, 2002.
21. N. Ogura and I. Yamada, "Non-strictly convex minimization over the fixed point set of the bounded fixed point set of the nonexpansive mapping," Numer. Funct. Anal. Optim., vol.24, nos.1&2, pp.129-135, 2003.
22. J. Okello, S. Arita, Y. Itoh, Y. Fukui, and M. Kobayashi, "An adaptive algorithm for cascaded notch filter with reduced bias," IEICE Trans. Fundamentals, vol.E84-A no.2, pp.589-596, Feb. 2001.
23. H. Stark and Y. Yang, Vector Space Projection - A Numerical Approach to Signal and Image Processing, Neural Nets and Optics, John Wiley & Sons, 1998.
24. I. Yamada, "Approximation of convexly constrained pseudoinverse by Hybrid steepest descent method," Proc. 1999 IEEE International Symposium on Circuits and Systems, vol.5, pp.37-40, 1999.
25. I. Yamada, "Convex projection algorithm from POCS to hybrid steepest descent method," J. IEICE, vol.83, no.8, pp.616-623, Aug. 2000.
26. I. Yamada, "The hybrid steepest descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings," in Inherently Parallel Algorithm for Feasibility and Optimization, ed. D. Butnariu, Y. Censor, and S. Reich, Elsevier, 2001.
27. I. Yamada, N. Ogura, and N. Shirakawa, "A numerically robust hybrid steepest descent method for the convexly constrained generalized inverse problems," in Inverse Problems, Image Analysis, and Medical Imaging, ed. Z. Nashed and O. Scherzer, Contemporary Mathematics, vol.313, pp.269-305, Amer. Math. Soc., 2002.
28. I. Yamada, N. Ogura, Y. Yamashita, and K. Sakaniwa, "Quadratic optimization of fixed points of nonexpansive mappings in Hilbert space," Numer. Funct. Anal. Optim., vol.19, nos.1&2, pp.165-190, 1998.
29. D.C. Youla, "Generalized image restoration by the method of alternating orthogonal projections," IEEE Trans. Circuits Syst., vol.25, no.9, pp.694-702, 1978.
30. D.C. Youla and H. Webb, "Image restoration by the method of convex projections: Part 1 - Theory," IEEE Trans. Med. Imaging, vol.MI-1, no.2, pp.81-94, 1982.
31. E. Zeidler, Nonlinear Functional Analysis and Its Applications, III - Variational Methods and Optimization, Springer-Verlag, 1985.