The trust region affine interior point algorithm for convex and nonconvex quadratic programming

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1. 1. I. ADLER, M. G. C. RESENDE, G. VEIGA, An implementation of Karmarkar's algorithm for linear programming, Math. Programming, 1989, 44, pp. 297-335. Zbl0682.90061MR1028226
2. 2. I. ADLER, R. D. C. MONTEIRO, Limiting behavior of the affine scaling continuous trajectories for linear programming problems, Math. Programming, 1991, 50, pp. 29-51. Zbl0719.90044MR1098845
3. 3. E. R. BARNES, A variation on Karmarkar's algorithm for solving linear programming, Math Programming, 1986, 36, pp. 174-182. Zbl0626.90052MR866987
4. 4. F. DELEBECQUE, C. KLIMANN, S. STEER, Basile. Un système de CAO pour l'automatique, Version 3.0. Guide d'utilisation, INRIA, Mars 1989. 
5. 5. D. A. BAYER, J. C. LAGARIAS, The nonlinear geometry of linear programming: I Affine and projective trajectories, Trans, Amer. Math. Soc., 1989, (2), 314, pp. 499-526. Zbl0671.90045MR1005525
6. 6. M. BOUTHOU, Méthodes de points intérieurs pour l'optimisation des systèmes de grande taille, Thèse de Doctorat, Université Paris Dauphine, 1993. 
7. 7. J.-P. BULTEAU, J.-P. VIAL, A restricted trust region algorithms for unconstrained optimization, Optim. Theory and Appl., 1985, 47, n° 4, pp. 413-435. Zbl0556.90075MR818870
8. 8. E. CASAS, C. POLA, Dealing with degenerated cases in quadratic programs, RAIRO-Operations Research, 1994, 27, n° 4, pp. 401 à 426. Zbl0795.90048MR1250365
9. 9. I. I. DIKIN, Iterative solutions of problems of linear and quadratic programming, Soviet. Math. Doklady, 1967, 8, pp. 674-675. Zbl0189.19504
10. 10. C. C. GONZAGA, L. A. CARLOS, A primal affine scaling algorithm for linearly constrained convex programs, Report, Federal University of Rio de Janeiro. 
11. 11. C. C. GONZAGA, Convergence of the large step primal affine scaling algorithm for primal non-degenerate linear programs, Tech. Report, Federal University of Rio de Janeiro, Brazil. 
12. 12. M. D. HEBDEN, An algorithm for minimization using exact second derivatives. Atomic Energy Research, Establishment report TP 515, Harwell, England 1973. 
13. 13. N. KARMARKAR, A new polynomial time algorithm for linear programming, Combinatorica, 1984, 4, pp. 373-395. Zbl0557.90065MR779900
14. 14. M. KOJIMA, S. MIZUNO, A. YOSHISE, AN O (√nL) iteration potential reduction algorithm for linear complementarity problems, Math. Programming, 1991, 50, pp. 331-342. Zbl0738.90077MR1114235
15. 15. O. L. MANGASARIAN, A simple characterization of solution sets of convex programs, Oper. Res. Lett., 1988, 7, pp. 21-26. Zbl0653.90055MR936347
16. 16. N. MEGIDDO, M. SHUB, Boundary behavior of interior point algorithms for linear programming, Math. Oper, Res., 1989, 14, pp. 97-146. Zbl0675.90050MR984561
17. 17. R. D. C. MONTEIRO, I. ADLER, M. G. C. RESENDE, A polynomial time primal-dual affine scaling algorithm for linear and convex quadratic programming and its power series extensions, Math. Oper. Res., 1990, 15 (2). Zbl0714.90060MR1051568
18. 18. J. J. MORÉ, Recent developments in algorithms and software for trust region method, Born 1982, Springer Verlag. Zbl0546.90077MR717404
19. 19. R. SAIGAL, A three step quadratically convergent implementation of the primal affine scalling method, Technical Report 93-9, Department of Industrial and Operational Engineering, University of Michigan, Ann-Arbor, MI-48109-2117, USA. 
20. 20. J. SUN, A convergence proof of an affine-scaling algorithm for convex quadratic programming without nondegeneracy assumptions, Technical Report, Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL 60208, USA, 1990. Zbl0781.90073
21. 21. P. TSENG, Z. Q. LUO, On the convergence of the affine scaling algorithm, Technical Report, CICS-P-169, Center for Intelligent Control Systems, Massachusetts Institute of Technology (Cambridge, MA, 1989). Zbl0762.90052
22. 22. T. TSUCHIYA, Global convergence of the affine scaling methods for degenerate linear programming problem, Math. Programming, 1991, 52, pp. 377-404. Zbl0749.90051MR1148177
23. 23. T. TSUCHIYA, Global convergence of the affine scaling algorithm for the primal degenerate strictly convex quadratic programming problems, The Institute of Statistical Mathematics, Tokyo, Japan, Technical report n° 417. Zbl0793.90055
24. 24. T. TSUCHIYA, M. MURATMATSU, Global convergence of a long-step affine scaling algorithm for degenerate linear programming problems, Research Memorandum 423, the Institute of Statistical Mathematics, 4-6-7 Minami-Azabou, Minoto-Ku, Tokyo 106, Japan, 1992. Zbl0838.90081
25. 25. T. TSUCHIYA, R. D. C. MONTEIRO, Superlinear convergence of the affine scaling algorithm, Department of Systems and Industrial Engineering, University of Arizona, Tucson, Technical Report. Zbl0870.90083
26. 26. R. J. VANDERBEI, S. M. MEKETON, B. A. FREEDMAN, A modification of Karmarkar's linear programming algorithm, Algorithmica, 1986, 1, pp. 395-407. Zbl0626.90056MR880730
27. 27. Y. YE, E. TSE, An extension of Karmarkar's projective algorithm for convex quadratic programming, Math. Programming, 1989, 44, pp. 157-179. Zbl0674.90077MR1003558
28. 28. Y. YE, On affine scaling algorithms for nonconvex quadratic programming, Math. Prog., 1992, 56, 3, pp. 285-301. Zbl0767.90065MR1187254