Free Access
Issue
RAIRO-Oper. Res.
Volume 30, Number 1, 1996
Page(s) 31 - 49
DOI https://doi.org/10.1051/ro/1996300100311
Published online 10 February 2017
  • 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. 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. [Zbl: 0871.90074]
  • 3. J. E. FALK and R. M. SOLAND, An algorithm for separable non convex programming problems, Management Science, 1969, 75, pp. 550-569. [MR: 389214] [Zbl: 0172.43802]
  • 4. R. FLETCHER, Practical methods of Optimization (second edition), John Wiley & Sons, New York, 1991. [MR: 955799] [Zbl: 0905.65002]
  • 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. [Zbl: 0718.90054]
  • 6. P. E. GILL, W. MURRAY and M. H. WRIGHT, Practical optimization, Academic Press, 1981. [MR: 634376] [Zbl: 0503.90062]
  • 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. [MR: 1263590] [Zbl: 0755.90076]
  • 8. R. HORST and H. TUY, Global Optimization: Deterministic Approaches, Springer-Verlag, Berlin, New York, 2e edition, 1993. [MR: 1274246] [Zbl: 0704.90057]
  • 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. [MR: 906423] [Zbl: 0638.90081]
  • 10. J. J. MORE and D. C. SORENSEN, Computing a trust region step, SIAM J. Sel Statist. Comput., 1981. 4, pp.553-572. [MR: 723110] [Zbl: 0551.65042]
  • 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. [MR: 1329604] [Zbl: 0834.90101]
  • 12. P. M. PARDALOS, J. H. GLICK and J. B. ROSEN, Global optimization of indefinite quadratic problems, Computing, 1987, 39, pp. 281-291. [MR: 923455] [Zbl: 0627.65072]
  • 13. A.T. PHILLIPS and J. B. ROSEN, A parallel algorithm forconstrained concave quadratic global minimization, Mathematical Programming, 1988, 42, pp.412-448. [MR: 976130] [Zbl: 0665.90071]
  • 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. [MR: 1084425] [Zbl: 0723.90063]
  • 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. J. B. ROSEN, Minimization of linearly constrained concave function by partition of feasible domain, Math. Operations Research, 1983, 8, pp. 215-230. [MR: 707054] [Zbl: 0526.90072]
  • 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. [MR: 838476] [Zbl: 0597.90066]
  • 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. PHAM D. TAO, Convergence of subgradient method for Computing the bound norm of matrices, Linear Alg. and its Appl., 1984, 62, pp. 163-182. [MR: 761065] [Zbl: 0563.65029]
  • 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. [MR: 769247] [Zbl: 0531.65022]
  • 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. [Zbl: 0638.90087]
  • 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. 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. [MR: 1017958] [Zbl: 0634.49009]
  • 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. [Zbl: 0876.90071]
  • 25. H. TUY, Global minimization of a difference of two convex functions, Mathematical Programming Study, 1987, 30, pp. 150-182. [MR: 874136] [Zbl: 0619.90061]
  • 26. H. TUY, The complementary convex structure in global optimization, J. of Global Optimization, 1992, 2, pp.21-40. [MR: 1266894] [Zbl: 0787.90091]
  • 27. S. A. VAVASIS, Approximation algorithms for indefinite quadratic programming, Mathematical Programming, 1992, 57, pp. 279-311. [MR: 1195028] [Zbl: 0845.90095]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.