Subdivision of simplices relative to a cutting plane and finite concave minimization

Journal of Global Optimization

Volumn 9, Issue 1, 1996, Pages 65-93

  Nast, Michael ^a  

^a UNIVERSITY OF TRIER   (Germany)

Author keywords

Concave minimization branch and bound; Global optimization; Simplicial subdivisions; Triangulation

Indexed keywords

EID: 0002636601     PISSN: 09255001     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00121751     Document Type: Article

References (19)

1. Be85 Benson, H.P. (1985), A Finite Algorithm for Concave Minimization over a Polyhedron, Naval Research Logistics Quaterly, 32, pp. 165-177
2. Be95 Benson, H.P. (1995), Concave Minimization: Theory, Applications and Algorithms, in R. Horst and P.M. Pardalos (eds.), Handbook of Global Optimization, Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 43-148
3. BeSa94 Benson, H.P. and Sayin, S. (1994), A Finite Concave Minimization Algorithm Using Branch and Bound and Neighbor Generation, Journal of Global Optimization, 5, pp. 1-14
4. FaHo76 Falk, J.E. and Hoffman, K.L. (1976), A Successive Underestimation Method for Concave Minimization Problems, Mathematics of Operations Research, 1, pp. 251-259
5. FaSo69 Falk, J.E. and Soland, R.M. (1969), An Algorithm for Separable Nonconvex Programming Problems, Management Science, 15, pp. 550-569
6. Gr67 Grünbaum, B. (1967), Convex Polytopes, Wiley-Interscience, London
7. Ha91 Haiman, M. (1991), A Simple and Relatively Efficient Triangulation of the n-Cube, Discrete Computational Geometry, Vol. 6, No. 4, pp. 287-289
8. HaJa88 Hamami, M. and Jacobsen, S.E. (1988), Exhaustive Nondegenerate Conical Process for Concave Minimization on Convex Polytopes, Mathematics of Operations Research, 13, pp. 479-487
9. Ho76 Horst, R. (1976), An Algorithm for Nonconvex Programming Problems, Mathematical Programming, Vol. 10, pp. 312-321
10. HoPaTh95 Horst,R., Pardalos, P.M. and Thoai, N.V. (1995), Introduction to Global Optimization, Kluwer Academic Publishers, Dordrecht, The Netherlands
11. HoTh88 Horst,R. and Thoai, N.V. (1988), Modification, Implementation and Comparison of Three Algorithms for Globally solving Concave Minimization Problems, Computing, Vol. 42, pp. 271-289
12. HoTu93 Horst,R. and Tuy, H. (1993), Global Optimization (Deterministic Approaches), 2nd Edition, Springer, Berlin
13. Hu93 Hughes, R.B. (1993), Minimum-cardinality triangulations of the d-cube for d = 5 and d = 6, Discrete Mathematics, 118, pp. 75-118
14. HuAn93 Hughes, R.B. and Anderson, M.R. (1993), A triangulation of the 6-cube with 308 simplices, Discrete Mathematics, 117, pp. 253-256
15. PaSt82 Papadimitriou, C.H. and Steiglitz, K. (1982), Combinatorial Optimization: Algorithms and Complexity, Prentice-Hall, Englewood Cliffs, New Jersey
16. So74 Soland, R.M. (1974), Optimal Facility Location with Concave Costs, Operations Research, 22, pp. 373-382
17. TaBa85 Tam, B.T. and Ban, V.T. (1985), Minimization of a Concave Function Under Linear Constraints. Ekonomika i Matematicheskie Metody, 21, 709-714, (in Russian)
18. Tod76 Todd, M. J. (1976), The Computation of Fixed Points and Applications, Lecture Notes in Economics and Mathematical Systems, Vol. 124, Springer, Berlin
19. Tuy91 Tuy, H. (1991), Effect of the Subdivision Strategy on Convergence and Efficiency of Some Global Optimization Algorithms, Journal of Global Optimization, Vol. 1, Nr. 1, pp. 23-36