Une procédure de purification pour les problèmes de complémentarité linéaire, monotones
Abderrahim Kadiri; Adnan Yassine
RAIRO - Operations Research - Recherche Opérationnelle (2004)
- Volume: 38, Issue: 1, page 63-83
- ISSN: 0399-0559
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top- [1] J.F. Bonnans, J.C. Gilbert, C. Lemarechal and C. Sagastizabal, Optimisation Numérique. Aspects théoriques et pratiques. Springer-Verlag (1997). Zbl0952.65044MR1613833
- [2] J.F. Bonnans and C.C. Gonzaga, Convergence of interior point algorithms for the monotone linear complementarity problem. Math. Oper. Res. 21 (1996) 1-25. Zbl0846.90109MR1385864
- [3] R.W. Cottle, J.S. Pang and V. Venkateswaran, Sufficient matrices and the linear complementarity problem. Linear Algebra Appl. 114/115 (1989) 231-249. Zbl0674.90092MR986877
- [4] F. Facchinei, A. Fischer and C. Kanzow, On the identification of zero variables in a interior-point framework. SIAM J. Optim. 10 (2000) 1058-1078. Zbl0999.90044MR1777080
- [5] C.C. Gonzaga, Path-following methods for linear programming. SIAM Rev. 34 (1992) 167-224. Zbl0763.90063MR1166175
- [6] T. Illes, J. Peng, C. Roos and T. Terlaky, A strongly polynomial rounding procedure yielding a maximally complementary solution for linear complementarity problems. SIAM J. Optim. 11 (2000) 320-340. Zbl1010.90082MR1787263
- [7] J. Ji and A. Potra, Tapia indicators and finite termination of infeasible-interior-point methods for degenerate LCP, edited by J. Renegar, M. Shub and S. Smale. AMS, Providence, RI. Math. Numer. Anal., Lect. Appl. Math. 32 (1996) 443-454. Zbl0868.90121MR1421349
- [8] J. Ji, A. Potra and S. Huang, Predictor-corrector method for linear complementarity problems with polynomial complexity and superlinear convergence. JOTA 85 (1995) 187-199. Zbl0824.90129MR1330846
- [9] A. Kadiri, Analyse numérique des méthodes de points intérieurs pour les problèmes de complémentarité linéaire et la programmation quadratique convexe. Thèse de Doctorat, INSA de Rouen (2001).
- [10] C.T. Kelley, Iterative methods for linear and nonlinear equations. Frontiers Appl. Math. 16 (1995). Zbl0832.65046MR1344684
- [11] M. Kojima, S. Mizuno and A. Yoshise, A polynomial-time algorithm for a class of linear complementarity problems. Math. Program. 44 (1989) 1-26. Zbl0676.90087MR999720
- [12] M. Kojima, Y. Kurita and S. Mizuno, Large-step interior point algorithmsfor linear complementarity problems. SIAM J. Optim. 3 (1993) 398-412. Zbl0781.90085MR1215450
- [13] K. Kortanek and J. Zhu, New purification algorithms for linear programming. Naval Res. Logist 35 (1988) 571-583. Zbl0685.90070MR952507
- [14] K. Mcshane, Superlineary convergent -iteration interior-point algorithms for LP and the monotone LCP. SIAM J. Optim. 4 (1994) 247-261. Zbl0822.90102MR1273758
- [15] R. Monteiro and I. Adler, Interior path-following primal-dual algorithms, part II: Convex quadratic programming. Math. Program. 44 (1989) 43-66. Zbl0676.90039MR999722
- [16] R. Monteiro and S. Wright, Local convergence of interior-point algorithms for degenerate monotone LCP. Comput. Optim. Appl. 3 (1994) 131-155. Zbl0801.90110MR1273658
- [17] C.R. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity. Prentice-Hall. Englewood Cliffs, New Jersey (1982). Zbl0503.90060MR663728
- [18] F.A. Potra and R. Sheng, A superlineary convergent infeasible-interior-point algorithm for degenerate LCP. J. Optim. Theory Appl. 97 (1998) 249-269. Zbl0907.90261MR1625072
- [19] Y. Ye, On the finite convergence of interior point algorithms for linear programming. Math. Program. 57 (1992) 325-335. Zbl0794.90036MR1195030
- [20] Y. Ye, Interior Point Algorithms: Theory and Analysis. John Wiley, New York (1997). Zbl0943.90070MR1481160
- [21] Y. Ye and K.M. Anstreicher, On quadratic and convergence of a predictor-corrector algorithm for LCP. Math. Program. 62 (1993) 537-551. Zbl0799.90111MR1251890