Convergence and application of a decomposition method using duality bounds for nonconvex global optimization

Journal of Optimization Theory and Applications

Volumn 113, Issue 1, 2002, Pages 165-193

  Thoai, N V ^a  

^a UNIVERSITY OF TRIER   (Germany)

Author keywords

branch and bound schemes; decomposition; Global optimization; nonconvex optimization; nonlinear parametric optimization

Indexed keywords

BRANCH AND BOUND METHOD; DECOMPOSITION; DECOMPOSITION METHODS; PROBLEM SOLVING;

BRANCH AND BOUND SCHEMES; DECOMPOSITION METHODS; GLOBAL OPTIMISATION; MASTER PROBLEMS; NONCONVEX OPTIMIZATION; NONCONVEX-OPTIMIZATION; NONLINEAR PARAMETRIC OPTIMIZATION; OBJECTIVE FUNCTIONS; OPTIMIZATION PROBLEMS; PARAMETRIC OPTIMIZATION;

GLOBAL OPTIMIZATION;

EID: 0036245676     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1014865432210     Document Type: Article

References (32)

1. BENDERS, J. F., Partitioning Procedures for Solving Mixed-Variables Programming Problems, Numerische Mathematik, Vol. 4, pp. 238-252, 1962.
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. FLOUDAS, C. A., and AGGARWAL, A., A Decomposition Strategy for Global Optimum Search in the Pooling Problem, ORSA Journal on Computing, Vol. 2, pp. 225-235, 1990.
4. FLOUDAS, C. A., and VISWESWARAN, V., A Primal-Relaxed Dual Global Optimization Approach, Journal of Optimization Theory and Applications, Vol. 78, pp. 187-225, 1993.
5. HORST, R., and THOAI, N. V., Conical Algorithms for the Global Minimization of Linearly Constrained Decomposable Concave Minimization Problems, Journal of Optimization Theory and Applications, Vol. 74, pp. 469-486, 1992.
6. HORST, R., and THOAI, N. V., Constraint Decomposition Algorithms in Global Optimization, Journal of Global Optimization, Vol. 5, pp. 333-348, 1994.
7. HORST, R., and THOAI, N. V., Decomposition Approach for the Global Minimization of Biconcave Functions over Polytopes, Journal of Optimization Theory and Applications, Vol. 88, pp. 561-583, 1996.
8. MUU, L. D., and OETTLI, W., Method for Minimizing a Convex-Concave Function over a Convex Set, Journal of Optimization Theory and Applications, Vol. 70, pp. 377-384, 1991.
9. THOAI, N. V., A Global Optimization Approach for Solving the Convex Multiplicative Programming Problem, Journal of Global Optimization, Vol. 1, pp. 341-357, 1991.
10. THOAI, N. V., Canonical DC Programming Techniques for Solving a Convex Program with an Additional Constraint of Multiplicative Type, Computing, Vol. 50, pp. 241-253, 1993.
11. GEOFFRION, A. M., Duality in Nonlinear Programming: A Simplified Application-Oriented Development, SIAM Review, Vol. 13, pp. 1-37, 1971.
12. MANGASARIAN, O. L., Nonlinear Programming, Robert E. Krieger Publishing Company, Huntington, New York, 1979.
13. BEN-TAL, A., EIGER, G., and GERSHOVITZ, V., Global Minimization by Reducing the Duality Gap, Mathematical Programming, Vol. 63, pp. 193-212, 1994.
14. DUR, M., and HORST, R., Lagrange Duality and Partitioning Techniques in Non-convex Global Optimization, Journal of Optimization Theory and Applications, Vol. 95, pp. 347-369, 1997.
15. BANK, B., GUDDAT, J., KLATTE, D., KUMMER, B., and TAMMER, K., Nonlinear Parametric Optimization, Birkhäuser, Basel, Switzerland, 1983.
16. DANTZIG, G. B., FOLKMAN, J., and SHAPIRO, N., On the Continuity of the Minimum Set of a Continuous Function, Journal of Mathematical Analysis and Applications, Vol. 17, pp. 519-548, 1967.
17. FIACCO, A. V., Introduction to Sensitivity and Stability Analysis in Nonlinear Programming, Academic Press, New York, NY, 1983.
18. BERGE, C., Topological Spaces, Macmillan, New York, NY, 1963.
19. HOGAN, W. W., Point-to-Set Maps in Mathematical Programming, SIAM Review, Vol. 15, pp. 591-603, 1973.
20. HORST, R., and TUY, H., Global Optimization: Deterministic Approaches, 3rd Edition, Springer, Berlin, Germany, 1996.
21. HORST, R., PARDALOS, P. M., and THOAI, N. V., Introduction to Global Optimization, Kluwer, Dordrecht, Netherlands, 1995.
22. FALK, J. E., and HOFFMAN, K. L., A Successive Underestimation Method for Concave Minimization Problems, Mathematics of Operations Research, Vol. 1, pp. 251-259, 1976.
23. PHILIP, J., Algorithms for the Vector Maximization Problem, Mathematical Programming, Vol. 2, pp. 207-229, 1972.
24. BENSON, H. P., Optimization over the Efficient Set, Journal of Mathematical Analysis and Applications, Vol. 98, pp. 562-580, 1984.
25. DAUER, J. P., and FOSNAUGH, T. A., Optimization over the Efficient Set, Journal of Global Optimization, Vol. 7, pp. 261-277, 1995.
26. FÜLÖP, J., A Cutting Plane Algorithm for Linear Optimization over the Efficient Set, Generalized Convexity, Edited by S. Komlösi, T. Rapcsàk, and S. Schaible, Lecture Notes in Economics and Mathematical Systems, Springer, Berlin, Germany, Vol. 405, pp. 374-385, 1994.
27. LE-THI, H. A., PHAM, D. T., and MUU, L. D., Numerical Solution for Optimization over the Efficient Set by DC Optimization Algorithms, Operations Research Letters, Vol. 19, pp. 117-128, 1996.
28. MUU, L. D., and LUC, L. T., On Equivalence between Convex Maximization and Optimization over the Efficient Set, Vietnam Journal of Mathematics, Vol. 24, pp. 439-444, 1996.
29. HORST, R., and THOAI, N. V., Maximizing a Concave Function over the Efficient or Weakly-Efficient Set, European Journal of Operations Research, Vol. 117, pp. 239-252, 1999.
30. THOAI, N. V., Conical Algorithm in Global Optimization for Optimizing over Efficient Sets, Journal of Global Optimization, Vol. 18, pp. 321-336, 2000.
31. KONNO, H., and KUNO, T., Linear Multiplicative Programming, Mathematical Programming, Vol. 56, pp. 51-64, 1992.
32. THOAI, N. V., Duality Bound Method for the General Quadratic Programming Problem with Quadratic Constraints, Journal of Optimization Theory and Applications, Vol. 107, pp. 331-354, 2000.