Difference of convex solution of quadratically constrained optimization problems

European Journal of Operational Research

Volumn 148, Issue 2, 2003, Pages 349-362

  Van Voorhis, Tim ^a   Al Khayyal, Faiz A ^b  

^a IOWA STATE UNIVERSITY   (United States)

^b Georgia Institute of Technology   (United States)

Author keywords

Branch and bound; Difference of convex programming; Global optimization; Outer approximation

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; CONSTRAINT THEORY; GLOBAL OPTIMIZATION; QUADRATIC PROGRAMMING;

CONVEX PROGRAMMING;

OPERATIONS RESEARCH;

EID: 0037449231     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-2217(02)00432-0     Document Type: Article

References (13)

1. Al-Khayyal F.A., Larsen C., Van Voorhis T. A relaxation method for nonconvex quadratically constrained quadratic programs. Journal of Global Optimization. 6(3):1995;215-230.
2. Chen P.-C., Hansen P., Jaumard B. On-line and off-line vertex enumeration by adjacency lists. Operations Research Letters. 10(7):1991;403-409.
3. Hiriart-Urruty J.B. Generalized differentiability, duality and optimality for problems dealing with differences of convex functions. Ponstein J. Convexity and Duality in Optimization, Lecture Notes in Economics and Mathematical Systems, vol. 256. 1985;37-70 Springer-Verlag, Berlin, New York.
4. Horst R., Thoai N.V., Benson H.P. Concave minimization via conical partitions and polyhedral outer approximation. Mathematical Programming. 50(2, Ser. A):1991;259-274.
5. Horst R., Tuy H. Global Optimization. second ed. 1993;Springer-Verlag, Berlin.
6. Sherali H.D., Adams W.P. A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Programs, Nonconvex Optimization and its Applications, vol. 31. 1999;Kluwer Academic Publishers, Dordrecht/Boston/London.
7. Tuy H. A general deterministic approach to global optimization via d.c. programming. Hiriart-Urruty J.B. Fermat Days 1985: Mathematics for Optimization. 1986;137-162 Elsevier, Amsterdam.
8. Tuy H. Convex programs with an additional reverse convex constraint. Journal of Optimization Theory and Applications. 52(3):1987;463-485.
9. H. Tuy, Introduction to Global Optimization, Ph.D. course (manuscript), Department of Mathematics, Linköping University, Linköping, Sweden, 1992. Also, GERAD, Ecole Polytechnique, Montreal, Canada, 1994.
10. Tuy H. Canonical DC programming problem: Outer approximation methods revisited. Operations Research Letters. 18(2):1995;99-106.
11. Tuy H. D.C. optimization: Theory, methods and algorithms. Horst R., Pardalos P. Handbook of Global Optimization, Nonconvex Optimization and its Applications, vol. 2. 1995;149-216 Kluwer Academic Publishers, Dordrecht.
12. Tuy H. Convex Analysis and Global Optimization, Nonconvex Optimization and its Applications, vol. 22. 1998;Kluwer Academic Publishers, Dordrecht.
13. Tuy H., Thuong N.V. On the global minimization of a convex function under general nonconvex constraints. Applied Mathematics and Optimization. 18:1988;119-142.