Le problème de complémentarité linéaire semi-défini
The semidefinite linear complementarity problem
DOI:
https://doi.org/10.33993/jnaat382-907Abstract
In French.
Dans cet article on présente une synthèse sur les principaux travaux liés au problème de complémentarité linéaire semi-défini.
La présentation est donnée de façon à rendre le bagage utilisé pour ce problème comprehensible et permettant de nouveaux développements.
In English.
In this article we present a synthesis on the main works related to the problem of semi-defined linear complementarity.
The presentation is given in such a way as to make the notions used for this problem understandable and allow for new developments.
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Achache, M., Multidimensional primal-dual path-following interior point methods for linear programming and linear complementarity problems, Thèse de Doctorat d'Etat, Université Ferhat Abbas de Sétif 19000, Algérie, 2005.
Alizadeh. F, Haeberly. J.A. and Overton, O., Primal-dual interior point methods for semidefinite programming, Convergence rates, stability and numerical results, SIAM J. Optimization, 8, pp. 746-768, 1998, https://doi.org/10.1137/s1052623496304700 DOI: https://doi.org/10.1137/S1052623496304700
Cottle, R.W., Pang, J.S. and Stone, R., The linear complementarity problem, Academic Press, Boston, 1992, https://doi.org/10.1137/1.9780898719000 DOI: https://doi.org/10.1137/1.9780898719000
Gowda, M.S. and Song, Y., On semidefinite linear complementarity problem. Mathematical Programming, Series A, 88, pp. 575-587, 2000, https://doi.org/10.1007/pl00011387 DOI: https://doi.org/10.1007/PL00011387
Gowda, M.S., Song, Y. and Ravindran, G., Some interconnections between strong monotonicity, GUS and P properties in semidefinite linear complementarity problems, Linear algebras and its applications, 370, pp. 355-386, 2003, https://doi.org/10.1016/s0024-3795(03)00425-7 DOI: https://doi.org/10.1016/S0024-3795(03)00425-7
Gowda, M.S. and Song, Y., Some new results for the semidefinite linear complementarity problem, SIAM Journal on Matrix Analysis and Applications, 24 (1) pp. 25-39, 2003, https://doi.org/10.1137/s0895479800377927 DOI: https://doi.org/10.1137/S0895479800377927
Malik, M. and Mohan, S.R., Some geometrical aspects of semidefinite linear complementarity problems, Linear and multilinear algebras, 54 (1), pp. 55-70, 2006, https://doi.org/10.1080/03081080512331318463 DOI: https://doi.org/10.1080/03081080512331318463
Murty, K.G., Linear complementarity, linear and nonlinear programming, Heldermann Verlag, Berlin, 1988, https://doi.org/10.1137/1031068??? https://doi.org/10.1016/0377-2217(89)90500-6 DOI: https://doi.org/10.1137/1031068
Karamardian, S., The complementarity problem, Mathematical Programming, 2, pp. 107-129, 1972, https://doi.org/10.1007/bf01584538 DOI: https://doi.org/10.1007/BF01584538
Kojima, M., Shindoh, M. and Hara, S., Interior point methods for the monotone semidefinite linear complementarity in symetric matrices, SIAM J. Optimization, 7, pp. 86-125, 1997, https://doi.org/10.1137/s1052623494269035 DOI: https://doi.org/10.1137/S1052623494269035
Krislock, J., Numerical solution of semidefinite constrained least squares problems, Master thesis, the university of british columbia, Canada, 2003.
Parthasarthy, T., Raman, D.S. and Sriparna, B., Relationship between strong monotonicity property, P2-property, and the GUS-property in semidefinite linear complementarity problems, Mathematics of Operations Research, 27 (2) pp. 326-331, 2002, https://doi.org/10.1287/moor.27.2.326.319 DOI: https://doi.org/10.1287/moor.27.2.326.319
Song, Y, The P and globally uniquely solvable properties in semidefinite linear complementarity problems, PhD thesis, University of Maryland, USA, 2002.
Vandenberghe, L. and Boyed, S., Semidefinite programming, SIAM Review, 38, pp. 49-95, 1996, https://doi.org/10.1137/1038003 DOI: https://doi.org/10.1137/1038003
Zhang, F., Matrix theory, Springer-Verlag, New-York, 1999.
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