A new successive partition algorithm for concave minimization based on cone decomposition and decomposition cuts

Journal of Global Optimization

Volumn 29, Issue 2, 2004, Pages 191-224

  Porembski, Marcus ^a  

^a PHILIPPS UNIVERSITY MARBURG   (Germany)

Author keywords

Concave minimization; Cone decomposition; Decomposition cut; Successive partition

Indexed keywords

ALGORITHMS; FUNCTIONS; ITERATIVE METHODS; LINEAR PROGRAMMING; QUADRATIC PROGRAMMING; SET THEORY;

CONCAVE MINIMIZATION; CONE DECOMPOSITION; DECOMPOSITION CUT; SUCCESSIVE PARTITION;

GLOBAL OPTIMIZATION;

EID: 4544341977     PISSN: 09255001     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:JOGO.0000042113.68493.da     Document Type: Article

References (22)

1. Bali, S. (1973), Minimization of a Concave Function on a Bounded Convex Polyhedron, Ph.D. thesis, University of California at Los Angeles, California.
2. Benson, H.P. (1995), Concave minimization: Theory, applications and algorithms, in Horst, R. and Pardalos, P.M. (eds.), Handbook of Global Optimization, Kluwer, Dordrecht, pp. 43-148.
3. Benson, H.P. (1996), Deterministic algorithms for constrained concave minimization: A unified critical survey, Naval Research Logistics, 43, 765-795.
4. Benson, H.P. (1999), Generalized γ-valid cut procedure for concave minimization, Journal of Optimization Theory and Applications, 102, 289-298.
5. Bretthauer, K.M. and Cabot, V.A. (1994), A composite branch and bound, cutting plane algorithm for concave minimization over a polyhedron, Computers and Operations Research, 21, 777-785.
6. Bretthauer, K.M., Cabot, V.A. and Venkataramanan, M.A. (1994), An algorithm and new penalties for concave integer minimization over a polyhedron, Naval Research Logistics, 41, 435-454.
7. Cabot, A.V. (1974), Variations on a cutting plane method for solving concave minimization problems with linear constraints, Naval Research Logistics Quarterly, 21, 265-274.
8. Falk, J.E. and Soland, R.M. (1969), An algorithm for separable nonconvex programming problems, Management Science, 15, 550-569.
9. Horst, R. (1976), An algorithm for nonconvex problems, Mathematical Programming, 10, 312-321.
10. Horst, R. and Tuy, H. (1996), Global Optimization (Deterministic Approaches), 3rd edition, Springer, Berlin.
11. Jaumard, B. and Meyer, C. (1998), A simplified convergence proof for the cone partitioning algorithm, Journal of Global Optimization, 13, 407-416.
12. Kalantari, B. (1986), Quadratic functions with exponential number of local maxima, Operations Research Letters, 5, 47-49.
13. Konno, H. (1976a), A cutting plane algorithm for solving bilinear programs, Mathematical Programming, 11, 14-27.
14. Konno, H. (1976b), Maximization of a convex quadratic function under linear constraints, Mathematical Programming, 11, 117-127.
15. Locatelli, M. and Thoai, N.V. (2000), Finite exact branch-and-bound algorithms for concave minimization over polytopes, Journal of Global Optimization, 18, 107-128.
16. Mangasarian, O.L. (1969), Nonlinear Programming, McGraw-Hill, New York.
17. Pardalos, P.M. and Schnitger, G. (1988), Checking local optimality in constrained quadratic programming is NP-hard, Operations Research Letters, 7, 33-35.
18. Porembski, M. (1999), How to extend the concept of convexity cuts to derive deeper cutting planes, Journal of Global Optimization, 15, 371-404.
19. Tuy, H. (1964), Concave programming under linear constraints, Soviet Mathematics, 5, 1437-1440.
20. Tuy, H. (1991), Effect of the subdivision strategy on convergence and efficiency of some global optimization algorithms, Journal of Global Optimization, 1, 23-36.
21. Tuy, H. (1998), Convex Analysis and Global Optimization, Kluwer, Dordrecht.
22. Zwart, P.B. (1974), Global maximization of a convex function with linear inequality constraints, Operations Research, 22, 602-609.