Un problème d’approximation matricielle : quelle est la matrice bistochastique la plus proche d’une matrice donnée ?

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1. [1] H. Bauschke, Projections Algorithms and Monotone Operators. Ph.D. thesis, Simon Fraser University (1996). 
2. [2] H. Bauschke and J. Borwein, Dykstra’s alternating projection algorithm for two sets. J. Approx. Theory 79 (1994) 418–443. Zbl0833.46011
3. [3] H. Bauschke and J. Borwein, On projection algorithms for solving convex feasibility problems. SIAM Rev. 38 (1996) 367–426. Zbl0865.47039
4. [4] J.P. Boyle and R.L. Dykstra, A method for finding projections onto the intersection of convex sets in Hilbert spaces, in Advances in Order Restricted Statistical Inference, edited by R.L. Dykstra, T. Robertson and F.T. Wright. Springer-Verlag. Lect. Notes Statist. (1985) 28–47. Zbl0603.49024
5. [5] H. Brezis, Analyse fonctionnelle. Théories et Applications. Masson (1983). Zbl0511.46001MR697382
6. [6] P. Combettes, Hilbertian convex feasibility problem: Convergence of projection methods. Appl. Math. Optim. 35 (1997) 311–330. Zbl0872.90069
7. [7] R. Escalante, Dykstra’s algorithm for a constrained least-squares matrix problem. Numerical Linear Algebra Appl. 3 (1996) 459–471. Zbl0908.90207
8. [8] W. Glunt, T. Hayden, S. Hong and J. Wells, An alternating projection algorithm for computing the nearest Euclidian distance matrix. SIAM J. Matrix Anal. Appl. 11 (1990) 589–600. Zbl0728.65034
9. [9] W. Glunt, T. Hayden and R. Reams, The nearest “doubly stochastic” matrix to a real matrix with the same first moment. Numer. Linear Algebra Appl. 5 (1998) 475–482. Zbl0969.15007
10. [10] N.J. Higham, Matrix nearness problems and applications. In Applications of Matrix Theory, edited by M.J.C. Gover and S. Barnett. Oxford University Press (1989) 1–27. Zbl0681.65029
11. [11] N.J. Higham, Computing the nearest correlation matrix – a problem from finance. IMA J. Numer. Anal. 22 (2002) 329–343. Zbl1006.65036
12. [12] J.-B. Hiriart-Urruty and C. Lemaréchal, Convex analysis and minimization algorithms. Grundlehren der mathematischen Wissenchaften 305 & 306. Springer-Verlag, Berlin, Heidelberg (1993). (New printing in 1996). Zbl0795.49002
13. [13] R.B. Horn and C.R. Johnson, Matrix Analysis. Cambridge University Press (1985). (Reprinted in 1991, 1992). Zbl0576.15001MR832183
14. [14] R.N. Khoury, Closest matrices in the space of generalized doubly stochastic matrices. J. Math. Anal. Appl. 222 (1998) 562–568. Zbl0911.15013
15. [15] R. Rockafeller and R.J.-B. Wets, Variational Analysis. Grundlehren der mathematischen Wissenchaften 317. Springer-Verlag, Berlin, Heidelberg (1998). Zbl0888.49001MR1491362
16. [16] P. Takouda, Un problème d’approximation matricielle : quelle est la matrice bistochastique la plus proche d’une matrice donnée ? Technical report, Laboratoire MIP, Université Paul Sabatier, Toulouse 3, 2002. Research Report MIP 02–21. Accessible on the web at the url : http://mip.ups-tlse.fr/publi/2002.html. Submitted. 
17. [17] P. Takouda, Problèmes d’approximations matricielle linéaire conique : approches par projections et via optimisation sous contraintes de semi-définie positivité. Ph.D. thesis, Université Paul Sabatier - Toulouse III (Septembre 2003). 
18. [18] P. Takouda, Résolution d’un problème d’agrégation de préférence en approximant par des matrices bistochastiques. Mathématiques et Sciences Humaines, “Recherche opérationnelle et aide à la décision”, 41${}^e$ année 161 (2003) 77–97. Aussi rapport interne numéro 03–08, du laboratoire MIP de l’Université Paul Sabatier, Toulouse. 
19. [19] E. Zarantonello, Projections on convex sets in Hilbert spaces and spectral theory, in Contributions to Nonlinear Functionnal Analysis, edited by E.E. Zarantonello, number 27 in University of Wisconsin. Mathematics Research Center Publications, Academic Press, New york (1971) 1–38. Proceeding on the special session on Optimization and Nonlinear Analysis, Jerusalem (May 1995). Zbl0281.47043