On globally solving linearly constrained indefinite quadratic minimization problems by decomposition branch and bound method

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1. 1. LE T. H. AN, Analyse numérique des algorithmes de l'Optimisation d.c. Approches locales et globales. Codes et simulations numériques en grande dimension. Applications. Thèse de Doctorat de l'Université de Rouen, France, 1994. 
2. 2. LE T. H. AN, PHAM D. TAO and L. D. Muu, Numerical solution for Optimization over the Efficient set by d.c. optimization algorithm, To appear in Opérations Research Letters. Zbl0871.90074
3. 3. J. E. FALK and R. M. SOLAND, An algorithm for separable non convex programming problems, Management Science, 1969, 75, pp. 550-569. Zbl0172.43802MR389214
4. 4. R. FLETCHER, Practical methods of Optimization (second edition), John Wiley & Sons, New York, 1991. Zbl0905.65002MR955799
5. 5. C. A. FLOUDAS, P. M. PARDALOS, A collection of test problems for constrained global optimization algorithms, In G. Goos and J. HARTMANIS, editors, Lecture notes in Computer Science, 445, Springer-Verlag, 1987. Zbl0718.90054
6. 6. P. E. GILL, W. MURRAY and M. H. WRIGHT, Practical optimization, Academic Press, 1981. Zbl0503.90062MR634376
7. 7. R. HORST, T. Q. PHONG, N. V. THOAI and J. de VRIES, On solving a d.c. programming problem by a sequence of linear programs, 7. of Global Optimization, 1991, I, pp. 183-203. Zbl0755.90076MR1263590
8. 8. R. HORST and H. TUY, Global Optimization: Deterministic Approaches, Springer-Verlag, Berlin, New York, 2e edition, 1993. Zbl0704.90057MR1274246
9. 9. B. KALANTARI and J. B. ROSEN, Algorithm for global minimization of linearly constrained concave quadratic functions, Mathematics of Opérations Research, 1987 72, pp. 544-561. Zbl0638.90081MR906423
10. 10. J. J. MORE and D. C. SORENSEN, Computing a trust region step, SIAM J. Sel Statist. Comput., 1981. 4, pp.553-572. Zbl0551.65042MR723110
11. 11. L. D. Muu, T. Q. PHONG and PHAM DINH TAO, Decomposition methods for solving a class of nonconvex programming problems dealing with bilinear and quadratic functions, Computational Optimization and Application, 1995, 4, pp. 203-216. Zbl0834.90101MR1329604
12. 12. P. M. PARDALOS, J. H. GLICK and J. B. ROSEN, Global optimization of indefinite quadratic problems, Computing, 1987, 39, pp. 281-291. Zbl0627.65072MR923455
13. 13. A.T. PHILLIPS and J. B. ROSEN, A parallel algorithm forconstrained concave quadratic global minimization, Mathematical Programming, 1988, 42, pp.412-448. Zbl0665.90071MR976130
14. 14. A.T. PHILLIPS and J. B. ROSEN, A parallel algorithm forpartially separable non-convex global minimization: linear constraints, Annals of Operations Research, 1990, 25, pp. 101-118. Zbl0723.90063MR1084425
15. 15. T. Q. PHONG, Analyse numérique des algorithmes d'Optimisation globale. Codes et simulations numériques. Applications. Thèse de Doctorat de l'Université de Rouen, France, 1994. 
16. 16. J. B. ROSEN, Minimization of linearly constrained concave function by partition of feasible domain, Math. Operations Research, 1983, 8, pp. 215-230. Zbl0526.90072MR707054
17. 17. J. B. ROSEN and P. M. PARDALOS, Global minimization of large scale constrained quadratic problems by separable programming, Mathematical Programming, 1986, 34(2), PP. 163-174. Zbl0597.90066MR838476
18. 18. PHAM D. TAO, Contribution à la théorie de normes et ses applications à l'analyse numérique. Thèse de doctorat d'état es sciences, USMG, Grenoble, France, 1981. 
19. 19. PHAM D. TAO, Convergence of subgradient method for Computing the bound norm of matrices, Linear Alg. and its Appl., 1984, 62, pp. 163-182. Zbl0563.65029MR761065
20. 20. PHAM D. TAO, Algorithmes de calcul du maximum d'une forme quadratique sur la boule unité de la norme du maximum, Numerische Mathematik, 1985, 45, pp. 377-440. Zbl0531.65022MR769247
21. 21. PHAM D. TAO, Algorithms for solving a class of nonconvex optimization problems. subgradient methods , Fermat days 85. Mathematics for Optimization, Elsevier Science Publishers B. V. North-Holland, 1986. Zbl0638.90087
22. 22. PHAM D. TAO, Some new results in nonconvex nondifferentiable optimization. 6th French-German Conference on Optimization, Lambrech, Germany, 2/6-8/6 1991. 
23. 23. PHAM D. TAO and EL BERNOUSSI, Duality in d.c. (difference of convex functions) optimization. subgradient methods, Trends in Mathematical Optimization, volume 84 of International Series of Numerische Mathematik, Birkhauser, 1988. Zbl0634.49009MR1017958
24. 24. PHAM D. TAO and LE T. H. AN, D. C. (difference of convex functions) optimization algorithms (DCA) for globally minimizing nonconvex quadratic forms on euclidean balls and sphères, To appear in Opérations Research Letters. Zbl0876.90071
25. 25. H. TUY, Global minimization of a difference of two convex functions, Mathematical Programming Study, 1987, 30, pp. 150-182. Zbl0619.90061MR874136
26. 26. H. TUY, The complementary convex structure in global optimization, J. of Global Optimization, 1992, 2, pp.21-40. Zbl0787.90091MR1266894
27. 27. S. A. VAVASIS, Approximation algorithms for indefinite quadratic programming, Mathematical Programming, 1992, 57, pp. 279-311. Zbl0845.90095MR1195028