Duality bound method for the general quadratic programming problem with quadratic constraints

Journal of Optimization Theory and Applications

Volumn 107, Issue 2, 2000, Pages 331-354

  Thoai, N V ^a  

^a UNIVERSITY OF TRIER   (Germany)

Author keywords

Branch and bound algorithms; Duality bounds; General quadratic programming problem with quadratic constraints; Global optimization

Indexed keywords

BRANCH AND BOUND METHOD; CONSTRAINED OPTIMIZATION; LINEAR PROGRAMMING; PROBLEM SOLVING; QUADRATIC PROGRAMMING;

BOUND METHOD; BRANCH-AND-BOUND ALGORITHMS; DUALITY BOUND; GENERAL QUADRATIC PROGRAMMING PROBLEM WITH QUADRATIC CONSTRAINT; GLOBAL OPTIMISATION; LINEAR PROGRAMS; PROPERTY; QUADRATIC CONSTRAINT; QUADRATIC PROGRAMMING PROBLEMS; QUADRATICALLY CONSTRAINED QUADRATIC PROGRAMMING;

GLOBAL OPTIMIZATION;

EID: 0034348654     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1026437621223     Document Type: Article

References (18)

1. 1. THOAI, N. V., and TUY, H., Convergent Algorithms for Minimizing a Concave Function, Mathematics of Operations Research, Vol. 5, pp. 556-566, 1980.
2. 2. ROSEN, J. B., and PARDALOS, P. M., Global Minimization of Large-Scale Constrained Concave Quadratic Problems by Separable Programming, Mathematical Programming, Vol. 34, pp. 163-174, 1986.
3. 3. PARDALOS, P. M., and ROSEN, J. B., Constrained Global Optimization: Algorithms and Applications, Lecture Notes in Computer Science, Springer Verlag, Berlin, Gernmany, Vol. 268, 1987.
4. 4. HORST, R., PARDALOS, P. M., and THOAI, N. V., Introduction to Global Optimization, Kluwer, Dordrecht, Netherlands, 1995.
5. 5. HORST, R., and TUY, H., Global Optimization: Deterministic Approaches, 3rd Edition, Springer, Berlin, Germany, 1996.
6. 6. HORST, R., and THOAI, N. V., DC Programming: Overview, Journal of Optimization Theory and Applications, Vol. 103, pp. 1-43, 1999.
7. 7. BEN-TAL, A., EIGER, G., and GERSHOVITZ, V., Global Minimization by Reducing the Duality Gap, Mathematical Programming, Vol. 63, pp. 193-212, 1994.
8. 8. DÜR, M., and HORST, R., Lagrange Duality and Partitioning Techniques in Nonconvex Global Optimization, Journal of Optimization Theory and Applications, Vol. 95, pp. 347-369, 1997.
9. 9. THOAI, N. V., A Decomposition Method Using Duality Bounds for Nonconvex Optimization, Forschungsbericht 97/24, University of Trier, 1997.
10. 10. VANDENBERGHE, L., and BOYD, S., Semidefinite Programming, SIAM Review, Vol. 38, pp. 49-95, 1996.
11. 11. SHOR, N. Z., Nondifferentiable Optimization and Polynomial Problems, Kluwer, Dordrecht, Netherlands, 1998.
12. 12. NOWAK, I., A New Semidefinite Programming Bound for Indefinite Quadratic Forms over a Simplex, Journal of Global Optimization, Vol. 14, pp. 357-364, 1999.
13. 13. FLOUDAS, C. A., and VISWESWARAN, V., Quadratic Optimization, Handbook of Global Optimization, Edited by R. Horst and P. Pardalos, Kluwer, Dordrecht, Netherlands, pp. 217-269, 1995.
14. 14. AL-KHAYYAL, F. A., LARSEN, C., and VAN VOORHIS, T., A Relaxation Method for Nonconvex Quadratically-Constrained Quadratic Programs, Journal of Global Optimization, Vol. 6, pp. 215-230, 1995.
15. 15. HORST, R., and THOAI, N. V., A New Algorithm for Solving the General Quadratic Programming Problem, Computational Optimization and Applications, Vol. 5, pp. 39-48, 1996.
16. 16. RABER, U., A Simplicial Branch-and-Bound Method for Solving Nonconvex All-Quadratic Programs, Journal of Global Optimization, Vol. 13, pp. 417-432, 1998.
17. 17. AL-KHAYYAL, F. A., and FALK, J. E., Jointly Constrained Biconvex Programming, Mathematics of Operations Research, Vol. 8, pp. 273-286, 1983.
18. 18. AL-KHAYYAL, F. A., Jointly Constrained Bilinear Programs and Related Problems: An Overview, Computers and Mathematics with Applications, Vol. 19, pp. 53-62, 1990.