Stability of lagrangian duality for nonconvex quadratic programming. Solution methods and applications in computer vision
ESAIM: Modélisation mathématique et analyse numérique, Tome 31 (1997) no. 1, pp. 57-90.
@article{M2AN_1997__31_1_57_0,
     author = {Pham Dinh Tao and Thai Quynh Phong and Horaud, Radu and Quan, Long},
     title = {Stability of lagrangian duality for nonconvex quadratic programming. {Solution} methods and applications in computer vision},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {57--90},
     publisher = {Elsevier},
     volume = {31},
     number = {1},
     year = {1997},
     mrnumber = {1432852},
     zbl = {0878.65045},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1997__31_1_57_0/}
}
TY  - JOUR
AU  - Pham Dinh Tao
AU  - Thai Quynh Phong
AU  - Horaud, Radu
AU  - Quan, Long
TI  - Stability of lagrangian duality for nonconvex quadratic programming. Solution methods and applications in computer vision
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1997
SP  - 57
EP  - 90
VL  - 31
IS  - 1
PB  - Elsevier
UR  - http://www.numdam.org/item/M2AN_1997__31_1_57_0/
LA  - en
ID  - M2AN_1997__31_1_57_0
ER  - 
%0 Journal Article
%A Pham Dinh Tao
%A Thai Quynh Phong
%A Horaud, Radu
%A Quan, Long
%T Stability of lagrangian duality for nonconvex quadratic programming. Solution methods and applications in computer vision
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1997
%P 57-90
%V 31
%N 1
%I Elsevier
%U http://www.numdam.org/item/M2AN_1997__31_1_57_0/
%G en
%F M2AN_1997__31_1_57_0
Pham Dinh Tao; Thai Quynh Phong; Horaud, Radu; Quan, Long. Stability of lagrangian duality for nonconvex quadratic programming. Solution methods and applications in computer vision. ESAIM: Modélisation mathématique et analyse numérique, Tome 31 (1997) no. 1, pp. 57-90. http://www.numdam.org/item/M2AN_1997__31_1_57_0/

[1] J. R. Clermont, M. E. De La Lande, P. D. Tao and A. Yassine, 1991, Analysis of plane and axisymmetric flows of incompressible fluids with the stream tube method : Numerical simulation by trust region algorithm, Inter. J. for Numer. Method in Fluids, 13, pp. 371-399. | MR | Zbl

[2] J. R. Clermont, M. E. De La Lande, P. D. Tao and A. Yassine, 1992, Numerical simulation of axisymmetric converging using stream tube and a trust region optimization algorithm, Engineering Optimization, 19, pp. 187-281.

[3] O. Faugeras, 1992, What can be seen in three dimensions with an uncalibrated stereo rig ? In G. Sandini, editor, Proccedings of the 2nd European Conference on Computer Vision, Santa Margherita Ligure, Italy, pp. 563-578. Springer-Verlag, May. | MR

[4] O. D. Faugeras, 1992, 3D Computer Vision, M.I.T. Press.

[5] O. D. Faugeras, Q. T. Luong and S. J. Maybank, 1992, Camera Self-Calibration : Theory and Experiments, In G. Sandini, editor, Proceedings of the 2nd European Conference on Computer Vision, Santa Margherita Ligure, Italy, pp. 321-334, Springer-Verlag, May. | MR

[6] O. D. Faugeras and G. Toscani, 1987, Camera calibration for 3D computer vision, In Proceedings of International Workshop on Machine Vision and Machine Intelligence, Tokyo, Japan.

[7] R. Fletcher, 1980, Practical methods of Optimization, John Wiley, New York. | MR | Zbl

[8] D. M. Gay, 1981, Computing optimal constrained steps, SIAM J. Sci. Stat. Comput., 2, pp. 186-197. | MR | Zbl

[9] G. H. Golub and C. Van Loan, 1989, Matrix Computations, North Oxford Academic, Oxford. | MR | Zbl

[10] T. S. Huang and O. D. Faugeras, 1989, Some properties of the E matrix en two-view motion estimation, IEEE Transactions on PAMI, 11(12), pp. 1310-1312, December.

[11] M. D. Hebden, 1973, An algorithm for minimization using exact second derivatives. Tech. Rep. TP515, Atomic energy research etablishment (AERE), Harwell, England.

[12] K. Levenberg, 1944, A method for the solution of certain nonlinear problems in least squares, Quart. Appl. Math., 2. | MR | Zbl

[13] P. J. Laurent, 1972, Approximation et Optimisation, Hermann, Paris. | MR | Zbl

[14] D. W. Marquardt, 1963, An algorithm for least squares estimation of nonlinear parameters, SIAM J. Appl. Math., 11. | MR | Zbl

[15] J. J. Moré, 1978, The Levenberg-Marquardt algorithm : Implementation and theory. In G.A, Waston, editor, Lecture Notes in Mathematics 630, pp. 105-116. Springer-Verlag, Berlin-Heidelberg-New York. | MR | Zbl

[16] J. J. Moré, 1983, Recent developments in algorithm and software for trust region methods. In A.Bachem, M. Grötschel and B.Korte, editors, Mathematical Proramming, The state of the art, pp. 258-287. Springer-Verlag, Berlin. | MR | Zbl

[17] J. J. Moré and D. C. Sorensen, 1981, Computing a trust region step, SIAM J. Sci. Statist. Comput., 4, pp. 553-572. | MR | Zbl

[18] R. Mohr, L. Quan and F. Veillon, Relative 3D Reconstruction using multiples uncalibrated images, The International Journal of Robotics Research, (to appear).

[19] R. T. Rockafellar, 1970, Convex Analysis, Princeton university Press, Princeton. | MR | Zbl

[20] G. A. Shultz, R. B. Schnabel and R. H. Byrd, 1985, A family of trust region based algorithms for unconstrained minimization with strong global convergence properties, SIAM J. on Numer. Anal., 22, pp. 47-67. | MR | Zbl

[21] T. Q. Phong, R. Horaud, P. D. Tao and A. Yassine, Object Pose from 2-D to 3-D Point and Line Correspondences, International Journal of Computer Visions (to appear).

[22] D. C. Soresen, 1982, Newton's method with a model trust region modification, SIAM J. Numer. Anal., 19(2), pp. 409-426, avril. | MR | Zbl

[23] Pham Dinh Tao, 1989, Méthodes numériques pour la minimisation d'une forme quadratique sur une boule euclidienne. Rapport de Recherche, Université Joseph Fourier, Grenoble.

[24] Pham Dinh Tao and Le Thi Hoai An, 1993, Minimisation d'une forme quadratique sur une boule et une sphère euclidiennes. Stabilité de la dualité lagrangienne. Optimalité globale. Méthodes numériques. Rapport de Recherche, LMI, CNRS URA 1378, INSA-Rouen.

[25] Pham Dinh Tao, Le Thi Hoai An and Thai Quynh Phong, Numerical methods for globally minimizing a quadratic form over euclidean ball an sphere (submitted).

[25] Pham Dinh Tao, S. Wang and A. Yassine, 1990, Training multi-layered neural network with a trust region based algorithm, Math. Modell. Numer. Anal., 24 (4), pp. 523-553. | Numdam | MR | Zbl