Solving an inverse problem for an elliptic equation by d.c. programming

Journal of Global Optimization

Volumn 25, Issue 4, 2003, Pages 407-423

  Hoai An, Le Thi ^a   Dinh Tao, Pham ^a   Nho Hào, Dinh ^b,c  

^a UNIVERSITÉ ET INSA DE ROUEN   (France)

^b INSTITUTE OF MATHEMATICS   (Viet Nam)

^c VRIJE UNIVERSITEIT BRUSSEL   (Belgium)

Author keywords

branch and bound technique; d.c. programming; DCA; ill posed problem; inverse problem; Tikhonov regularization

Indexed keywords

EID: 84867939324     PISSN: 09255001     EISSN: 15732916     Source Type: Journal    
DOI: 10.1023/A:1022530520406     Document Type: Article

References (28)

1. Bui, H. D. (1994), Inverse Problems in the Mechanics of Materials, CRC Press, Boca Raton, FL.
2. G. Chavent K. Kunisch 1994 Convergence of Tikhonov regularization for constrained ill-posed inverse problems Inverse Problems 10 63 76
3. F. Colonius K. Kunisch 1986 Stability for parameter estimation in two point boundary value problem J. Reine Angewandte Math. 370 1 29
4. F. Colonius K. Kunisch 1989 Output least squares stability in elliptic systems Appl. Math. Opt. 19 33 63
5. Engl, H. W., Hanke, M. and Neubauer, A. (1996), Regularization of Inverse Problems, Kluwer Academic Publishers, Dordrecht.
6. J. E. Falk R. M. Soland 1969 An algorithm for separable nonconvex programming problems Management Science 15 550 569
7. B. Kalantari J. B. Rosen 1987 Algorithm for global minimization of linearly constrained concave quadratic functions Mathematics of Operations Research 12 544 561
8. H.W. Engl K. Kunisch A. Neubauer 1989 Convergence rates for Tikhonov regularisation of non-linear ill-posed problems Inverse Problems 5 523 540
9. Groetsch, Ch. W. (1993), Inverse Problems in the Mathematical Sciences. Friedr. Vieweg & Sohn, Braunschweig.
10. Horst, R. and Tuy, H. (1993), Global Optimization: Deterministic Approaches, 2 edition, Springer, Berlin, New York.
11. Isakov, V. (1998) Inverse Problems for Partial Differential Equations, Springer, New York.
12. J. B. Keller 1976 Inverse problems Amer. Math. Monthly 83 107 118
13. K. Kunisch W. Ring 1993 Regularization of nonlinear ill-possed problems with closed operators Numer. Funct. Anal. Optimiz. 14 389 404
14. Ladyzhenskaya, O. A. (1985), The Boundary Value Problems of Mathematical Physics, Springer, New York, Berlin, Heidelberg, Tokyo.
15. Le Thi Hoai An (1997), Contribution à l'optimisation non convexe et l'optimisation globale: Théorie, Algorithmes et Applications, Habilitation à Diriger des Recherches, Université de Rouen.
16. L. T. H. An P. D. Tao 1997 Solving a class of linearly constrained indefinite quadratic problems by d.c. algorithms Journal of Global Optimization 11 253 285
17. L. T. H. An P. D. Tao 1998 A branch-and-bound method via d.c. optimization algorithm and ellipsoidal technique for box constrained nonconvex quadratic programming problems Journal of Global Optimization 13 171 206
18. Le Thi Hoai An and Pham Dinh Tao (2001), The D.C. programming and DCA revisited with D.C. models of real world nonconvex optimization problems, Proceedings of The 5th International Conference on Optimization: Techniques and Applications, Hong Kong December 15-17, 2001 (ICOTA 2001) Editor D. Li, Volume 3, pp. 1324-1333.
19. Le Thi Hoai An and Pham Dinh Tao (2002), Large Scale Global Molecular Optimization from exact distance matrices by a d.c. optimization approach, Revised version in SIAM Journal on Optimization.
20. Le Thi Hoai An, Pham Dinh Tao, and Dinh Nho Hào (2001), On the ill-posedness of the trust region subproblem. Journal of Inverse and Ill-Posed Problems (to appear)
21. Le Thi Hoai An, Pham Dinh Tao, and Dinh Nho Hào (2001), D.c. programming approach to Tikhonov regularization for non-linear ill-posed problems, (in preparation).
22. Pham Dinh Tao and E. B. Souad (1986), Algorithms for solving a class of non convex optimization problems. Methods of subgradients, Fermat days 85. Mathematics for Optimization, Elsevier, North-Holland, Amsterdam: 249-270.
23. P. D. Tao E. B. Souad 1988 Duality in d. c. (difference of convex functions) optimization. Subgradient methods Trends in Mathematical Optimization, International Series of Numer Math. 84 277 293
24. P. D. Tao L. T. H. An 1998 D.c. optimization algorithms for solving the trust region subproblem SIAM J. Optimization 8 476 505
25. P. D. Tao L. T. H. An 1997 Convex analysis approach to d.c. programming: Theory, Algorithms and Applications Acta Mathematica Vietnamica 22 1 289 355
26. Polyak, B. (1987), Introduction to Optimization. (Optimization Software Inc., Publication Division, New York.
27. Rockafellar, R. T. (1970), Convex Analysis, Princeton University Press, Princeton.
28. Tikhonov, A. N., Leonov, A. S. and Yagola, A. G. (1998), Non-linear Ill-Posed Problems, Vol. 1, 2, Chapman and Hall, London.